Function Composition

Key Questions

• Is function composition associative?

  Answer:

  Yes

  Explanation:

  Given composable functions #f#, #g# and #h#

  #(f@(g@h))(x)#

  #= f((g@h)(x)) = f(g(h(x))) = (f@g)(h(x))#

  #= ((f@g)@h)(x)#

  So #f@(g@h) = (f@g)@h#

  George C. · 1 · Jul 24 2015
• What is the domain of #(f@g)(x)#?

  Answer:

  If #g:A->B# and #f:B->C#, then the domain of #f@g# is

  #bar(g)^(-1)@bar(f)^(-1)(C)#

  using the notation described below...

  Explanation:

  If #g# is a function that maps some elements of a set #A# to elements of a set #B#, then the domain of #g# is the subset of #A# for which #g(a)# is defined.

  More formally:

  #g sube A xx B :#

  #AA a in A AA b_1, b_2 in B#

  #((a, b_1) in g ^^ (a, b_2) in g) => b_1 = b_2#

  Use the notation #2^A# to represent the set of subsets of #A# and #2^B# the set of subsets of #B#.

  Then we can define the pre-image function:

  #bar(g)^(-1): 2^B -> 2^A# by #bar(g)^(-1)(B_1) = {a in A : g(a) in B_1}#

  Then the domain of #g# is simply #bar(g)^(-1)(B)#

  If #f# is a function that maps some elements of set #B# to elements of a set #C#, then:

  #bar(f)^(-1): 2^C -> 2^B# is defined by #bar(f)^(-1)(C_1) = {b in B : f(b) in C_1}#

  Using this notation, the domain of #f@g# is simply

  #bar(g)^(-1)(bar(f)^(-1)(C)) = (bar(g)^(-1)@bar(f)^(-1))(C)#

  George C. · 1 · Jul 24 2015
• What are some examples of function composition?

  To compose a function is to input one function into the other to form a different function. Here's a few examples.

  Example 1: If #f(x) = 2x + 5# and #g(x) = 4x - 1#, determine #f(g(x))#

  This would mean inputting #g(x)# for #x# inside #f(x)#.

  #f(g(x)) = 2(4x- 1) + 5 = 8x- 2 + 5 = 8x + 3#

  Example 2: If #f(x) = 3x^2 + 12 + 12x# and #g(x) =sqrt(3x)#, determine #g(f(x))# and state the domain

  Put #f(x)# into #g(x)#.

  #g(f(x)) = sqrt(3(3x^2 + 12x + 12))#

  #g(f(x)) = sqrt(9x^2 + 36x + 36)#

  #g(f(x)) = sqrt((3x + 6)^2)#

  #g(f(x)) = |3x + 6|#

  The domain of #f(x)# is #x in RR#. The domain of #g(x)# is #x > 0#. Hence, the domain of #g(f(x))# is #x > 0#.

  Example 3: if #h(x) = log_2 (3x^2 + 5)# and #m(x) = sqrt(x + 1)#, find the value of #h(m(0))#?

  Find the composition, and then evaluate at the given point.

  #h(m(x)) = log_2 (3(sqrt(x + 1))^2 + 5)#

  #h(m(x)) = log_2 (3(x + 1) + 5)#

  #h(m(x)) = log_2 (3x + 3 + 5)#

  #h(m(x)) = log_2 (3x + 8)#

  #h(m(2)) = log_2 (3(0) + 8)#

  #h(m(2)) = log_2 8#

  #h(m(2)) = 3#

  Practice exercises

  For the following exercises: #f(x) = 2x + 7, g(x) = 2^(x - 7) and h(x) = 2x^3 - 4#

  a) Determine #f(g(x))#

  b) Determine #h(f(x))#

  c) Determine #g(h(2))#

  Hopefully this helps, and good luck!

  Noah G · 1 · Dec 22 2016

• What is function composition?
• What are some examples of function composition?
• What are some common mistakes students make with function composition?
• Is function composition associative?
• Is it always true that #(f@g)(x) = (g@f)(x)#?
• If #f(x) = x + 3# and #g(x) = 2x - 7#, what is #(f@g)(x)#?
• If #f(x) = x^2# and #g(x) = x + 2#, what is #(f@g)(x)#?
• If #f(x) = x^2# and #g(x) = x + 2#, what is #(g@f)(x)#?
• What is the domain of #(f@g)(x)#?
• What is the domain of the composite function #(g@f)(x)#?
• If #f(x) = x/6 - 2# and #g(x) = 6x + 12#, how can I show #(f@g)(x) = (g@f)(x)#?
• If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(f@g)(x)#?
• If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(g@f)(x)#?
• If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(f@g)(0)#?
• If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(g@f)(-3)#?
• How do you write the area a of a circle as a function of its circumference?
• How do you determine #f(g(x))# if #ƒ(x)=x(x + 1)# and #g(x)=x^2−1#?
• If #f(x)=x^2+4x# and #g(x)=3x-5#, how do you find #(f(g(x))# and #g(f(x))#?
• Given #f(x)= x^5+x^3+x#, how do you find the inverse f(3) and f(f inverse (2))?
• If #f(x+1) =2x# and #g(3x) = x+6#, how do you find the value of #f^-1(g(f(13)))3?
• Let #h(x) = x/(x+4)# and #k(x)=2x-4#, how do you find (hºk)(x) and simplify?
• Let #h(t) = (2-t)/(t)# and #g(t)= (3t+15)/t#, how do you find (h/g)(t) and the domain for h/g?
• Let #f(x)=2x+3# and #g(x)=x^2-4# and #h(x)=x-3/2#, how do you find f(g(3))?
• Let #f(x)=2x+3# and #g(x)=x^2-4# and #h(x)=x-3/2#, how do you find g(f(3))?
• Let #f(x)=2x+3# and #g(x)=x^2-4# and #h(x)=x-3/2#, how do you find f(h(x))?
• Let #f(x)=x+2# and #g(x)=sqrtx#, how do you find g(f(x))?
• Let # f(x)= -4x+3# and #g(x)= 1/(x+2)#, how do you evaluate f(g(x)) and g(f(x)) for x?
• Let #u(x)=e^(9x)# and #v(x)=5x+9#, how do you find #(v(u(x)))^2#?
• Let #f(x)=1-x# and #g(x)= x^2# and #h(x)= 1/x#, how do you find #f(g(x))#?
• Let #f(x)=1-x# and #g(x)= x^2# and #h(x)= 1/x#, how do you find g(h(x))?
• Let #f(x)=1-x# and #g(x)= x^2# and #h(x)= 1/x#, how do you find g(f(h(x)))?
• Let #f(x)=1-x# and #g(x)= x^2# and #h(x)= 1/x#, how do you find f(h(g(x)))?
• Let #f(x) = 1 /(x+3)# and #g(x) = -2 /x#, how do you find each of the compositions?
• Let #f(x)= 1/(x-3)#, how do you find f(f(x))?
• Let # f(x)=ln(0.5x) # and #g(x)=e^(3x)#, how do you find each of the compositions?
• Let # f(x) = x^2 # and ##, how do you find each of the compositions?
• Let #g(x) = 3x – 1# and #f(x) = 5x + 2#, how do you find each of the compositions?
• Let #u(x)=2x-1# and #w(x)=x^2#, how do you find u(w(-4)) and w(u(-4))?
• Let #f(x) = 1/x# and #g(x) = sqrt(x-2)#, how do you find each of the compositions and domain and range?
• Let #f(x) = -1 /(x - 7)# and #g(x) = 8-x^2#, how do you find each of the compositions and domain and range?
• Let #f(x)=8x # and #g(x)=x/8#, how do you find each of the compositions and domain and range?
• Let #f(x) = x + 8# and #g(x) = 3x#, how do you find each of the compositions and domain and range?
• Let #f(x) = 1/x^2# and #g(x) = x−1#, how do you find each of the compositions and domain and range?
• Let #F(x)=6-x# and #g(y)=sqrty#, how do you find each of the compositions and domain and range?
• Let #F(x)=3x# and #g(y)=1/y#, how do you find each of the compositions and domain and range?
• Let #h(t) = 1/(t^2)# and #g(t)= sqrt(3t+5)#, how do you find each of the compositions and domain and range?
• Let #F(x)=2/(x-1)# and #G(x)=1/(x+3)#, how do you find each of the compositions and domain and range?
• Let #f(x) = 1 + 2x# and #g(x) = x/(x-1)#, how do you find each of the compositions and domain and range?
• Let #f(x) = 2 -x# and #f(g(x)) = (2x-3)/x#, how do you find g(x)?
• Let # f(x) = (3x -1) /( x - 2 )# and #f(g(x)) =x#, how do you find g(x)?
• Let # f(x) = 4x -3# and #g(f(x)) = 1/(4x)#, how do you find g(x)?
• Let #f(x)=x^2-4 # and #g(x)=sqrt(x-3)#, how do you find each of the compositions?
• Let # f(x) = 3/(x-1)# and #g(x) = 2/x#, how do you find each of the compositions?
• Let #f(x)= 1-x^3# and #g(x)= 1/x#, how do you find each of the compositions?
• How do you verify that f(x) and g(x) are inverses: #f(x) = x+7#, #g(x) = x-7#?
• If f(x) = 2x-1 and g(x) = 1/x how do you determine x such that f(g(x)) = g(f(x))?
• How do you solve this function : g[f(x)] if #f(x) = 4x + 1# and #g(x)=2x^2 - 5 = 2x^2 - 5#?
• How do you write #y = (x − 11)^5# as a composition of two simpler functions?
• How do you write # y = 3sqrt(1 + x^2)# as a composition of two simpler functions?
• How do you write #y = 2(x − 3)^5 − 5(x − 3)^2 + 0.5(x − 3) + 11# as a composition of two simpler functions?
• How do you write #y = 1/(x^2 + 3)# as a composition of two simpler functions?
• How do you write # y = sqrt(sqrt(x) + 1)# as a composition of two simpler functions?
• How do you write #y = 2 - sqrt(5 - (3x - 1)^2)# as a composition of two simpler functions?
• Let f(x)=8x-1, and g(x)=x/2 how do you find (fg(x))?
• Let f(x) = 5x + 2 and g(x) = 2x - 1 how do you find (fog)(x)?
• Let f(x) = 8x-1 and g(x) = x/2 how do you find (fog)(x)?
• Let #f(x) =abs(x+1)# and g(x) = 3x-2 how do you find (fog)(x)?
• Let #f(x) =7x+4# and g(x) = x-7 how do you find (fog)(x)?
• Let #f(x) = (1) / (1-3x) # and #g(x) = (1) / (x^2) # how do you find f(g(x)?
• How do you write #h(x) = cos(x^2)# as a composition of two or more functions?
• How do you write #j(x) = sin^2(x)# as a composition of two or more functions?
• How do you write #k(x) = e^sinx# as a composition of two or more functions?
• How do you write #l(x) = (tan(x^2))^.5# as a composition of two or more functions?
• If #f(x)=x^2+1# and #g(x)=x-2#, how do you find f[g(x)]?
• If #f(x)=3x# and #g(x)=4x-3#, how do you find f[g(5)] and g[f(5)]?
• How do you find #f(g(x-3))# if #g(x) = x + 3# and #f(x) = x^2 - 2#?
• How do you find #f(g(x))# if #f(x) = (x-3) / (5x+1)# and #g(x) = (x-1) / (x^2)#?
• How do you find #g(f(x))# if #g(x) = x^2# and #f(x) = x + 3#?
• How do you find #f(g(4))# if #f(x)=2sqrt(x+3)# and #g(x)=-3x+1#?
• How do you find [f • g](x) and [g • f](x) if #F(x)= 2x + 7# and #G(x) = -5x - 1#?
• How do you find [f • g](x) and [g • f](x) if #F(x) = x^2 - 1# and #g(x) = -4x^2#?
• How do you find [f • g](x) and [g • f](x) if #F(x) = x^2 + 2x# and #G(x) = x-9#?
• How do you find (f of g of h) if #f(x)=x^2+1# #g(x)=2x# and #h(x)=x-1#?
• How do you find [g of h](x) if #g(x)=8-2x# and #h(x)=3x#?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find (f+g)(x)?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find (g-f)(x) ?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find (f*g)(x)?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find (f/g)(x)?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find g(f(x))?
• Given the functions #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2# how do you find h(g(x))?
• Given the functions #g(x) = 3/(x - 1)#, #f(x) = (x - 1)/(x - 3)# what is g(f(x))?
• Given the functions #f(x) = x^2# and #g(x) = 3x+2# what is f(g(x))?
• Given the functions #g(x) = (2x) (1/2)#, #f(x) = x^2 + 1 # what is f(g(x))?
• Given the functions #F(x)=x+4# and #G(x)=2x^2+4# what is f(g(x))?
• How do you find the inverse of #p(x)=x^3-3x^2+3x-1#?
• How do you graph the piecewise function #x, if -2 < x < 2#, #2x, if x < -2#, #3x, if x > 2#?
• How do you graph the piecewise function #3x+2 , if x ≠ 1#, #8 , if x = 1#?
• How do you find the domain and range of the piecewise function #y = x^2 if x < 0#, #y = x + 2 if 0 ≤ x ≤ 3#, #y = 4 if x >3#?
• Given the piecewise function #f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}#, how do you evaluate f(-4)?
• Given the piecewise function #f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}#, how do you evaluate f(-3)?
• Given the piecewise function #f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}#, how do you graph it?
• Given the piecewise function #y = { sqrt(-x), -4 ≤ x ≤ 0, sqrtx ,0 < x ≤ 4#, how do you find the domain?
• Given the piecewise function # 1-x,x<-1#, #(x^2)-x,-1<=x<=6#, #x-7,x>6#, is it continuous at x=-1 and -6?
• Given the piecewise function #f(x)= 3,x<=0#, #2, if x> 0#, how do you evaluate f(2)?
• Given the piecewise function #f(x)= 3,x<=0#, #2, if x> 0#, how do you evaluate f(-4)?
• Given the piecewise function #3-x, x<=2#, #x^2, x >2#, how do you evaluate f(6)?
• Given the piecewise function #3-x, x<=2#, #x^2, x <2#, how do you evaluate f(2)?
• How do you write write #f(x)=|x-4|# as a piecewise function?
• How do you find the inverse of #f(x)=In(3-2x)+3#?
• How do you find the inverse of #f(x)=(2x+1)/x#?
• How do you find the inverse of #f(x) = x^2 +7#?
• How do you find the inverse of #f(x) =(x + 2)^2 - 4#?
• How do you find the inverse of #f(x) =e^(2x-1)#?
• How do you find the inverse of #H(x)=log x#?
• How do you find the inverse of #f(x)= (2x+1)/(x-3)#?
• How do you find the inverse of #f(x)=(7/x)-3#?
• How do you find the inverse of #f(x) = (2x-1)/(x-1)#?
• How do you find the inverse of #y = Arctan(x+pi/2)#?
• How do you find the inverse of #f(x)=(e^x)/x#?
• How do you find the inverse of #f(x) = x / (x + 8)#?
• How do you find the inverse of #f(x) = root5((3 x - 5) / (x - 5)) #?
• How do you find the inverse of #f(x) = 4(x + 5)^2 - 6#?
• How do you find the inverse of #f(x)= x^5+x^3+x#?
• How do you find the inverse of #f(x)= absx + 1#?
• How do you find the inverse of #f(x)=3x^4#?
• How do you find the inverse of #f(x)=2-2x^2#?
• How do you find the inverse of #f(x) = x^2 +x#?
• How do you find the inverse of #f(x) = x^2 + x - 2#?
• How do you find the inverse of #f(x)=(2-3x)/4#?
• How do you find the inverse of #f(x) = 1-x^3#?
• How do you find the inverse of #f(x) = 1-x^3#?
• How do you find the inverse of #f(x)=3^(x+2)#?
• How do you find the inverse of #f(x) = 3x + 1#?
• How do you find the inverse of #f(x) = (x - 2) / (x + 2)#?
• How do you find the inverse of #f(x)=(x-4)^2#?
• How do you find the inverse of #y=x^3 +5#?
• How do you find the inverse of #f(x)=x/5+4 #?
• How do you find the inverse of #y=x^2+2x-1#?
• How do you find the inverse of #f(x)=2x+3#?
• How do you find the inverse of #f(x)=4x-1#?
• How do you find the inverse of # f(x) = x^2 + 9#?
• How do you find the inverse of #f(x) =(3x + 1) / -x#?
• What is the inverse of #y=6#?
• How do you find the inverse of #y=log(3x-1)#?
• How do you find the inverse of #H(x)=log x#?
• How do you find the inverse of # f(x) = 3log(x-1)#?
• How do you find the inverse of # y=log_2 2x#?
• How do you find the inverse of #y=log_3 (4x)#?
• How do you find the inverse of #f(x)= -log_5 (x-3)#?
• How do you find the inverse of #f(x)=log[x+1]#?
• How do you find the inverse of #y = 2^x#?
• How do you find the inverse of #y=log_8x#?
• How do you find the inverse of #y=e^(x-1)#?
• How do you find the inverse of #y=-log_5(-x) #?
• How do you find the inverse of #f(x)=log(x+7)#?
• How do you find the inverse of #log 2^-x#?
• How do you find the inverse of #f(x) =2x-5#?
• How do you find the inverse of #f(x) =1/x#?
• How do you find the inverse of #f(x) =10^x#?
• How do you find the inverse of #y=log(x+2)#?
• How do you find the inverse of #y=log_8(x+2)#?
• How do you find the inverse of #g(x) =log ((x)/(1-x))#?
• How do you find the inverse of #y = log_5x#?
• How do you find the inverse of #y = 3^x#?
• How do you find the inverse of #y =1/logx#?
• How do you find the inverse of #g(x)= log_3(x+2)-6#?
• How do you find the inverse of #y = -log_4x#?
• How do you find the inverse of #y=log(x+4)#?
• How do you find the inverse of #y=log_6 x+5 #?
• How do you find the inverse of #y=log_5 (x+2) #?
• How do you find the inverse of #y=log_4( x/2 +3 )#?
• How do you find the inverse of #log _(1/2) (x+4)=y#?
• How do you find the inverse of #log _ 1.25 (x)=y#?
• How do you find the inverse of #y=log_5(x+4)+1#?
• How do you find the inverse of #y=log( -3x) +2#?
• How do you find the inverse of #f(x)=2^(x+1) -2#?
• How do you find the inverse of #f(x)=2log(x+1)#?
• How do you find the inverse of #y=log_x4#?
• How do you find the inverse of #y=log_2x#?
• How do you find the inverse of #y=log_2(x+4)#?
• How do you find the inverse of #y=log(4x)#?
• How do you find the inverse of #f(x)=log_3(x-4)-2#?
• How do you find the inverse of #f(x)=-(1/3)^x#?
• How do you find the inverse of #f(x) = x/(x+1)#?
• How do you find the inverse of #f(x) =3(2^x)#?
• How do you find the inverse of #y=log_6 x#?
• How do you find the inverse of #f(x)=3^(x-1)-2#?
• How do you find the inverse of #y=10^x#?
• How do you find the inverse of #y=ln(8x + 1)#?
• How do you find the inverse of # f(x)=x+4#?
• How do you find the inverse of # f(x)=e^-x#?
• How do you find the inverse of #f(x) = 200*3^(x/4) #?
• How do you find the inverse of #y=ln(x+2)#?
• How do you find the inverse of #f(x) = 3 ln (x-2)#?
• How do you find the inverse of #f(x) =ln(x^2)#?
• How do you find the inverse of #y = ln x#?
• How do you find the inverse of #f(x) =ln(4x-1)#?
• How do you find the inverse of #f(x)=x/(x+9)#?
• How do you find the inverse of #3^(2x)?
• How do you find the inverse of #f(x) = 5x - 3#?
• How do you find the inverse of #f(x)= x/(x-9)#?
• How do you find the inverse of #y=log_9 x#?
• How do you find the inverse of #y=log_(1/4) x#?
• How do you find the inverse of #y=log_(1/2) x#?
• How do you find the inverse of #y=log_7 49^x#?
• How do you find the inverse of #y=e^x#?
• How do you find the inverse of #f(x)=2-3 log_4(x+1)#?
• How do you find the inverse of #f(x)=7^(2x+7)#?
• How do you find the inverse of #y=ln(x-1)-6#?
• How do you find the inverse of #y=4^x#?
• How do you find the inverse of #f(x) = 4/x#?
• How do you find the inverse of #y = 1/3log(2x+5) - 4#?
• How do you find the inverse of #f(x)= 1- ln(x-2)#?
• How do you find the inverse of #f(x)=ln (3-2x)+3#?
• How do you find the inverse of #y = e^x/(1 + 4 e^x)#?
• How do you find the inverse of #f(x)= (100)/(1+2^-x)#?
• How do you find the inverse of #y = -logx#?
• How do you find the inverse of #y=log(50x)#?
• How do you find the inverse of # f(x)=log(x+15)#?
• How do you find the inverse of #1-ln(x-2)=f(x)#?
• How do you find the inverse of #f(x)=ln(x-1) - ln(2x +1)#?
• How do you find the inverse of #y=ln(3x+1)#?
• How do you find the inverse of #y=log_(6)x#?
• How do you find the inverse of #f(x)=50,000(0.8)^x#?
• How do you find the inverse of #y=log_3 9x#?
• How do you find the inverse of #f(x)= x/(x-9)#?
• How do you find the inverse of #f(x)=2x+ln(x)#?
• How do you find the inverse of #f(x) = 18 + ln(x)#?
• How do you find the inverse of #h(x)=8x#?
• How do you find the inverse of #g(x)=(x-5) / 2#?
• How do you find the inverse of #f(x)=x^7#?
• How do you find the inverse of #f(x)=(x-1)/(x+2)#?
• How do you find the inverse of #f(x)=10x#?
• How do you find the inverse of #f(x) = ln(5x)#?
• How do you find the inverse of #f(x)=(2x-3)/(x+1)#?
• How do you find the inverse of # y = ln(x + 4)#?
• How do you find the inverse of # y =sqrt(x-4)#?
• How do you find the inverse of #y = (e^x)/(1+2e^x)#?
• How do you find the inverse of #f(x) = (2x)/(x-1)#?
• How do you find the inverse of #g(x)=x^3-1#?
• How do you find the inverse of #2x+3=y#?
• How do you find the inverse of #y=e^x/(1+6e^x)#?
• How do you find the inverse of #y=ln(x/(x-1))#?
• How do you find the inverse of #f(x)=(e^x)+1#?
• How do you find the inverse of #f(x) = 2log (3x-12) + 5#?
• How do you find the inverse of #y = log (x/2)#?
• How do you find the inverse of #y = 5x + 20#?
• How do you find the inverse of #y=ln(x+4)#?
• How do you find the inverse of #y=(1/2)^x#?
• How do you find the inverse of #y=(4x+2)/(x-7)#?
• How do you find the inverse of #g(x)= 2x-4#?
• How do you find the inverse of #f(x) = log7^x#?
• How do you find the inverse of #f(x) = 5^x#?
• How do you find the inverse of #f(x) = -log2^x#?
• How do you find the inverse of #f(x) = 5^x#?
• How do you find the inverse of #f(x) = log 2^x#?
• How do you find the inverse of #y = (log_2 x) +2#?
• How do you find the inverse of #f(x)=e^x-1#?
• How do you find the inverse of #f(x)=1/x^2#?
• How do you find the inverse of #f(x) = (1-2x) / (1+x)#?
• How do you find the inverse of #f(x)=3^(x+2)#?
• How do you find the inverse of #y=2(3)^x +1#?
• How do you find the inverse of #y= 2^(1.5x+3)#?
• How do you find the inverse of #y=e^(3x+1)#?
• How do you find the inverse of #y = x^2 + 9#?
• How do you find the inverse of #f(x)= (x+5)^3-7#?
• How do you find the inverse of #y = 3^x#?
• How do you find the inverse of #y=e^(3x)+2#?
• How do you find the inverse of #y=6^(x)+1#?
• How do you find the inverse of #f(x) = e^x - e^-x#?
• How do you find the inverse of #g(x)= log_8(4 x+6)#?
• How do you find the inverse of # y=1/(x-3)#?
• How do you find the inverse of #f(x)=7#?
• How do you find the inverse of #f(x)=(x+2)^2-4#?
• How do you find the inverse of #f(x)=3sqrt(x+2)#?
• How do you find the inverse of #y=log_6x#?
• How do you find the inverse of #y=log_3x#?
• How do you use composition of functions to show that #f(x)=(2+x)/x# and #f^-1(x) = 2/(x-1)# are inverses?
• If #F(x)= x+2# and #G(x)= x/2#, how do you determine if the composition of functions is commutative?
• How do you find the inverse of #f (x) = 1/3 x +2 #?
• How do you find (f o g)(x) if #g(x) = (x^2 -16)^(1/2)#, #f(x) = (3 - x)^(1/2)#?
• How do you determine the three functions f, g, and h such that #(f o g o h)(x) = sin^2(x+1)#?
• How do you find the compositions given #f(x) = x/(x^2+1)#, #g (x) = x^2 +1#?
• How do you find g(h(t)) given #g(t) = (t+1)/2#, #h(t) = (t-3)/4#?
• How do you find #(f@g)(x)# given #g(x) = (2x) (1/2)#, #f(x) = x^2 + 1 #?
• How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)) give #f(x) = x^2#, #g(x) = ln(x)#?
• How do you find g[h(x)] and h[g(x)] given #h(x)=2x-1# #g(x)=3x+4#?
• How do you find the (f o g o h) (x) for #f(x)=(x-2)/(2x+1), #g(x)=3x+1#, #h(x)=x^2#?
• How do you find (g o f)(x) given #f(x)= x/(x-2)#, #g(x)=3/x#?
• How do you find (g o f)(x) when #f(x)=2x# and #g(x)=x^3+x^2+1#?
• How do you find s[h(x)] if #s(x) = 2^x# and #h(x) = x^2#?
• How do you find [f o g](2) and [gof](2)] given #f(x)=2x-1#, #g(x)=-3x#?
• How would you show that #f (x) = 7x +3# and #f^-1(x) = (x +3 )/ 7# are inverses of each other?
• How do you find g[f(x)] if #g(x) = x^2# and #f(x) = x + 3#?
• How do you express the following function, f(x) as a composition of two functions f and g given #f(x)=x^2/(x^2+4)#?
• How do you solve this function : g[f(x)] if f(x) = 4x + 1 and #g(x) = 2x^2 - 5#?
• How do you express the following function, f(x) as a composition of two functions f and g #f(x)=x^2/(x^2+4)#?
• Given #f(x) = (3-2x) / (2x+1)# and #f(g(x)) = 7 - 3x# how do you find g(x)?
• Given #f(x) = 3x - 2x#, #g(x) = sqrtx# and #h(x) = 3x^2 + 2# how do you find (g o f)(-2)?
• Given #f(x)=8x-1#, and #g(x)=x/2# how do you find fog(x)?
• How do you find #(fg)(5)+f(4)# when #f(x)=(x^2)+1# and #g(x)=x-4#?
• Given #f(x) = 7x^2 - 5x#, #g(x) = 17x - 4# how do you find (fog)(6)?
• Given #f(x) = -6x + 7#, #g(x) = 3x + 2# how do you find (gof)(x)?
• Given #f(x) = |2x + 1|#, #g(x) = 3x³ -1# how do you find f(g(x))?
• How do you find the composition of function given #f(x)= sqrt (x+8)# and #g(x)= 4x + 1#?
• How do you express the function #h(x)=(x + 3)^6# in the form f o g?
• What is the difference between (fo(goh)(x) and ((fog)oh)(x)?
• Given #f(x)=6/x^2# and #g(x)=x-3#, how do you find g(f(x))?
• How do you write the combined function as a composition of several functions if #f(g(x)) = sqrt (1-x^2) +2#?
• If #f(x)= 1-x^3# and #g(x)= 1/x# how do you find f(g(x))?
• Let #s(x) = x ^2 + 2x + 3x# and #t(x) = sqrt(x+4), how do you find sot(6)?
• How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)), given #f(x) = x^2# and #g(x) = ln(x) #?
• How do you find (f of g of h) given #f(x)=x^2+1# #g(x)=2x# and #h(x)=x-1#?
• How do you find [g of h](x) given #g(x)=8-2x# and #h(x)=3x#?
• How do you find the function compositions given #f(x)= 2x-3# and #g(x)=3x#?
• How do you find the function compositions given # f(x)= x^2#, #g(x)= 5x#?
• How do you find the function compositions given #g(x)=x^2-2# and #h(x)=sqrt(5-x)#?
• How do you express the function #y=x^2+3# as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)?
• How do you compute (fog) and (gof) if #f(x) = (3x-1) / (2x+5)# and #g(x) =(7x+3) / (3x-1)#?
• How do you compute (fog) and (gof) if #f(x)= x/(x-2)#, #g(x)=3/x#?
• How do you compute (fog) and (gof) if #g(x) = 3x#, #f(x) = x +1#?
• How do you compute (fog) and (gof) if #g(x) = x^2 - 8#, #f(x) = (-x +1)^(1/2)#?
• How do you write the composite function in the form f(g(x)) #y = sin(7x)#?
• How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem #f(x) = 2x + 3#, #g(x) = 3x -1#?
• How do you find #(f @ g)(x)# and its domain, #(g @ f)(x)# and its domain,# (f @ g)(-2) # and #(g @ f)(-2)# of the following problem #f(x) = x+ 2#, #g(x) = 2x^2#?
• How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem #f(x) = x^2 – 1#, #g(x) = x + 1#?
• How do you find the compositions given #f(x) = 5x + 2 # and #g(x) = 2x - 1 #?
• How do you find the compositions given # f(x)=8x-1# and #g(x)=x/2#?
• How do you find the compositions given # f(x) =x^2 + 2x + 1# and #g(x) = x - 2#?
• How do you find the compositions given #f(x) = |x + 1|# and #g(x) = 3x - 2 #?
• How do you find the compositions given #f(x)=7x+4# and #g(x)=x-7#?
• How do you find the compositions given #f(x)=8x# and #g(x)=x/8#?
• How do you find the compositions given #f(x) = x+4/3 # and #g(x) = 3x-4#?
• How do you find the compositions given #f(x)+3x-5# and #g(x)= sqrt(x-2)#?
• How do you find the compositions given #f(x) = x/(x + 1)#, #g(x) = x^2 - 1#?
• How do you find the compositions given #f(x)=3x²# and #g(x)=4-5x#?
• How do you find the compositions given #f(x)= sqrt(x-2)# and #g(x)= x^2-1#?
• How do you find the compositions given #g(x)=4x-1# and #h(x)=sqrt(x+3)#?
• How do you find the compositions given #f(x)=4x^2#, #g(x)=-x+3#?
• How do you find the compositions given #g(x) = 3x + 2# and #h(x) = 9x^2 + 12x + 9#?
• How do you find the compositions given #f(x) = 2x + 3# and #h(x) = 2x^2 + 2x + 1#?
• How do you find the compositions given # f(x)=x+2# and #g(x)= sqrtx#?
• How do you find the compositions given #f(x)=-3x+5#, #g(x)=1+2x-x^2#?
• How do you find the compositions given #f(x)=2-x# and #g(x)=2/(5-x)#?
• How do you find the compositions given #f(x)=x^2# and #g(x)=sqrtx #?
• How do you find the compositions given #f(x) = |x - 2#|, #g(x) = sqrtx#?
• How do you find the compositions given #f(x)=x + 5#, #g(x)= 2x#, #h(x)= x-2#?
• How do you find the compositions given #f(x)=x-7# , #g(x)=x^2# and #h(x)=(x-7)^2#?
• How do you find the compositions given #F(x)=x+4# and #g(x)=x^2#?
• How do you find the compositions given #f(x) = 1/(1+x)# and #g(x) = sqrt(x+2)#?
• How do you find the compositions given #f(x)=3x^2-6x+5# and #g(x)=x^2+5x-2#?
• How do you find the compositions given #f(x)= 5/(x-6)# and #g(x) = 4/5x#?
• How do you find the compositions given #f(x)=x^3+2# and #g(x)=root3(x-2)#?
• How do you find the compositions given #g(x) = x^2 + 2# and #f(x) = 2x#?
• How do you find the compositions given #f(x)=sqrt(x-3)#, #g(x)=sqrt(x +3)#?
• How do you find the inverse of #y=4x+7#?
• How do you find the inverse of #y = -(1/3)^x #?
• How do you find the inverse of #f^-1(x)= -2 - 1/(x-1)#?
• How do you find the inverse of #y=2x^(2)-12x#?
• How do you find the inverse of #f(x) = 3x + 1# and is it a function?
• How do you find the inverse of #h(x)=-3x+6# and is it a function?
• How do you find the inverse of #f(x) = | x | - 3# and is it a function?
• How do you find the inverse of #y=4/(x+4)# and is it a function?
• How do you find the inverse of #y=x^2# and is it a function?
• How do you find the inverse of #y=1-6x^3-3# and is it a function?
• How do you find the inverse of #f(x) = (2x-3)/(x+4)# and is it a function?
• How do you find the inverse of #y = 13/x # and is it a function?
• How do you find the inverse of # y = -13/x# and is it a function?
• How do you find the inverse of #y = 2^x# and is it a function?
• How do you find the inverse of #f(x)=sqrt(x+1) + 3# and is it a function?
• How do you find the inverse of #f(x)=4^x# and is it a function?
• How do you find the inverse of #Y=5X-1# and is it a function?
• How do you find the inverse of #e^-x# and is it a function?
• How do you find the inverse of #y = log_5x# and is it a function?
• How do you find the inverse of #g(x) = x^2 + 4x + 3 # and is it a function?
• How do you find the inverse of #f(x) = 2x-4# and is it a function?
• How do you find the inverse of # (x + 2)^2 - 4# and is it a function?
• How do you find the inverse of #y=3-7x# and is it a function?
• How do you find the inverse of #f(x)=x^3-2# and is it a function?
• How do you find the inverse of #y = x + 4# and is it a function?
• How do you find the inverse of #f(x)=x^2+2x-5# and is it a function?
• How do you find the inverse of #f(x)= -|x+1|+4# and is it a function?
• How do you find the inverse of #f(x) = 3 ln (x-2)# and is it a function?
• How do you find the inverse of #y=1/x# and is it a function?
• How do you find the inverse of #y=3x^2-2# and is it a function?
• How do you find the inverse of #f(x) = x – 7# and is it a function?
• How do you find the inverse of #f(x) = 3^x# and is it a function?
• How do you find the inverse of #y=x^3 +5# and is it a function?
• How do you find the inverse of #f(x) =2x-5# and is it a function?
• How do you find the inverse of #f(x) =x^3-2# and is it a function?
• How do you find the inverse of #f(x) =1/(4x+7)# and is it a function?
• How do you find the inverse of #f(x) =10^x# and is it a function?
• How do you find the inverse of #f(x) = (x + 2)^2# and is it a function?
• How do you find the inverse of #f(x) = 1/3x +2# and is it a function?
• How do you find the inverse of #(2x+7)/(3x-1)# and is it a function?
• How do you find the inverse of # y= log_2 (x+4)# and is it a function?
• How do you find the inverse of #f(x)=3x-5# and is it a function?
• How do you find the inverse of #f(x) = sqrt (x-2)# and is it a function?
• How do you find the inverse of #f(x)=3x^2-6x+1# and is it a function?
• How do you find the inverse of #y=6x+3# and is it a function?
• How do you find the inverse of #f(x)=2x+3# and is it a function?
• How do you find the inverse of #x^2 +3# and is it a function?
• How do you find the inverse of #y=-3x+1# and is it a function?
• How do you find the inverse of #y=2x-4# and is it a function?
• How do you find the inverse of #f(x)=(x+3)^(1/2) + 2# and is it a function?
• How do you find the inverse of #f(x)=9 x-4# and is it a function?
• How do you find the inverse of #y = x/(x+1)# and is it a function?
• How do you find the inverse of #y=x^(2)-6x+4# and is it a function?
• How do you find the inverse of #y = (x+3)/(x-2)# and is it a function?
• How do you find the inverse of #y=4^x# and is it a function?
• How do you find the inverse of #f(x) = 1 - (1/x)# and is it a function?
• How do you find the inverse of #f(x) = 4/x# and is it a function?
• How do you find the inverse of #f(x)=x^2-2x-8# and is it a function?
• How do you find the inverse of #f(x) = x^3 + 2x# and is it a function?
• How do you find the inverse of #f(x)= 2/(x+1)# and is it a function?
• How do you find the inverse of #y = 3x-9# and is it a function?
• How do you find the inverse of #f(x)= x^3+x# and is it a function?
• How do you find the inverse of # f(x) = (2x-1)/(x-1)# and is it a function?
• How do you find the inverse of #y= -x# and is it a function?
• How do you find the inverse of #y = 2x^2 - 3x +1# and is it a function?
• How do you find the inverse of #arctan(x+3)# and is it a function?
• How do you find the inverse of #f(x)= (1/2)x + 4# and is it a function?
• How do you find the inverse of #h(X)= 5 / (2x + 3)# and is it a function?
• How do you find the inverse of #h(x)= x^2 - 4x + 5# and is it a function?
• How do you find the inverse of #h(x)= x^3 - 3x^2 + 3x - 1# and is it a function?
• How do you find the inverse of #y = 2^(3 - x)# and is it a function?
• How do you find the inverse of #f(x)= 1/3x + 2# and is it a function?
• How do you find the inverse of #y= x^2-2x+1# and is it a function?
• How do you find the inverse of #y=3x^2+x# and is it a function?
• How do you find the inverse of #y=4-x^2+3x# and is it a function?
• How do you find the inverse of #y=((x^2)-4)/x# and is it a function?
• How do you find the inverse of #h(x)=(5x+1)/4# and is it a function?
• How do you find the inverse of #f(x)=x^2 - 1# and is it a function?
• How do you find the inverse of #f(x) = x/(x+1)# and is it a function?
• How do you find the inverse of #y=log_2 2x# and is it a function?
• How do you find the inverse of #y=(x+3)²-5# and is it a function?
• How do you find the inverse of #y=-2(x+3)²+# and is it a function?
• How do you find the inverse of #f(x)=sqrt(3x) # and is it a function?
• How do you find the inverse of #ln(x^2)# and is it a function?
• How do you find the inverse of # ln(8x + 1) # and is it a function?
• How do you find the inverse of # p(x)=x^3-3x^2+3x-1# and is it a function?
• How do you find the inverse of #2x-2# and is it a function?
• How do you find the inverse of #f(x)=(x+2)/(x-1)# and is it a function?
• How do you find the inverse of # x - 2y = 5# and is it a function?
• How do you find the inverse of #g(x)=5x-2# and is it a function?
• How do you find the inverse of #f(x) = x^2 + x# and is it a function?
• How do you find the inverse of #e^(2x )# and is it a function?
• How do you find the inverse of #f(x) = 3x – 6 # and is it a function?
• How do you find the inverse of #y=cos x +3 # and is it a function?
• How do you find the inverse of #y=sinx# and is it a function?
• How do you find the inverse of #f(x) = x^2 + 2# and is it a function?
• How do you find the inverse of #y = 3^x# and is it a function?
• How do you find the inverse of #f(x) = x^3 + 5# and is it a function?
• How do you find the inverse of # f(x) = (x + 2)^2# and is it a function?
• Given #f(x) = (x-3) / (5x+1)# and #g(x) = (x-1) / (x^2)# how do you find f(g(x))?
• Given #f(x) = sqrt(42-x) # and #g(x) = x^2 - x# how do you find f(g(x)) and what is it's domain?
• Given #if f(x)=x^2-4# and #g(x)=sqrt(x-3)# how do you find f(g(x)) and g(f(x))?
• Given # f(x) = x^2 + 1 # and #g(x) = (2x) (1/2)# how do you find f(g(x))?
• Given #f(x)=x+2# and #g(x)=x-2# how do you find f(g(x))?
• Given #f(x)=x^3+2# and #g(x)=root3(x-2)# how do you show they are inverses?
• Given #f(x) = (3x-1 )/( 2x+5)# and #g(x)=( 7x+3 )/( 3x-1)# how do you find f(g(x))?
• Given #f(x)= sqrt (x+8)# and #g(x)= 4x + 1# how do you find f(g(x)) and g(f(x))?
• Let #f(x)=x^2-4# and #g(x)=sqrtx+3#, how do you find f(g(x))?
• Let #f(x)=x^2-4# and #g(x)=sqrtx+3#, how do you find g(f(x))?
• How do you find f(x+h) for the function f(x)= x - 4?
• How do you find f(x+h) for the function #f(x)= x^2 - 2x + 5#?
• How do you find f(x+h) for the function #f(x)= x^3 + x#?
• How do you find 2p(a) + p(a-1) for the function #p(x) = 4x + 1#?
• How do you find 2p(a) + p(a-1) for the function #p(x)= x^2 - 5x + 8#?
• How do you find 2p(a) + p(a - 1) if #p(x) = x^2 + x#?
• For the function #f(x)= 7e^x# how do you find the following function values: f(-1)?
• For the function #f(x)= 7e^x# how do you find the following function values: f(0)?
• For the function #f(x)= 7e^x# how do you find the following function values: f(1)?
• For the function #f(x)= 7e^x# how do you find the following function values: f(3)?
• If #f(x)=x^2 + 2x +3#, then how do you find f(a-1)?
• How many subgroups does the group #(ZZ_5, o+_5)# have ?
• Let #f(x) = 7x^2+5# and g(x) = x-3, how do you find the composite function (f o g)(2)?
• If#""f^2(x)+g^2(x)+h^2(x)<=9# and #u_x=3f(x)+4g(x)+10h(x)#, again #(u_x)_"max"=sqrtn,"where"" "ninN# then what is the value of n?
• Given #y= (x-3)^5 +2#, how do you find f(x) and g(x) so that the function can be described as y=f(g(x))?
• How do you find #f ^-1(x)# given #f(x) = (x+1)/(x+2)# when x ≠ -2?
• How do you find g o f which is g(f(x)) when f(x)=x^2-2 and g(x)=1/(x-2)?
• How do you find #f@g# which is #f(g(x))# when #f(x)=x^2-2# and #g(x)=1/(x-2)#?
• How do you find the inverse of # y = e^x-1/x#?
• If #-f(x) + f(x-1) = 3x# and #f(1)=1000#, what is #f(20)# ?
• If #f(x)=mx-2# , #g(x)=(3x+2n)/6# and #(g@f)(x)# is a unit function, what is #m+n# ?
• How do you find #(fog)(x)# given #f(x)=2x^3-5x^2# and #g(x)=2x-1#?
• How would you find #f^-1# and verify that #f(f^-1(x))=f^-1(f(x))=x#, if #f(x)=2x+3#? #f(x)=x^3+1#?
• Given that #f(x)=x^2-4x# and #g(x)=x+3#, what is #(f∘g)(1)#?
• Question #6c5fe
• How does this simpify?
• The two functions t(x) and v(x) are defined below. t(x)=6x-1 v(x)=x^2+2 Evaluate the composition of functions v(t(4))?
• F(x)=1/2x; g(x)=1/3x find f(g(x) and g(f(x) State domain of each Precalculus questions?
• What is the difference between x-intercepts, zeros, and roots?
• Let #f(x)=x^2-12# and #g(x)=15-x#, how do you find #(f/g)(5)#?
• How do I find the inverse of #f(x)=(x+3)/(x-2)#?
• How do I find the inverse of #f(x)=(x-5)^2#?
• What is the domain of #fog(x)# given #f(x)=sqrt(x-2)# and #g(x)=1/(2x)#?
• How do you find the inverse of each function #y=x^2-12#?
• If #f(x)=-2x+7# and #g(x)=x+2#, what is #f * g#?
• If #f(x)=-2x+11# and #g(x)=x-6#, how do you find #[fog](x)# and #[gof](x)#?
• If #g(x)=-2x^2-5x# and #h(x)=3x+2#, how do you find #g(h(x))#?
• If #f(x)=x+3# how do you find the inverse?
• If #f(x)=x^2-3# and #g(x)=5x#, how do you find f(g(-3))?
• If #g(x)=x^2+5x+4# and #f(x)=x-2#, how do you find g(f(-2))?
• How do you evaluate #f(-3)# given #f(x)=4x^3+x^2-5x#?
• How do you evaluate #g(m+1)# if #g(x)=2x^2-4x+2#?
• How do you evaluate #f(3)# given #f(x)=2x+3#?
• How do you evaluate #g(-2)# if #g(x)=5x^2+3x-2#?
• How do you evaluate #h(0.5)# if #h(x)=1/x#?
• How do you evaluate #j(2a)# if #j(x)=1-4x^3#?
• How do you evaluate #f(n-1)# if #f(x)=2x^2-x+9#?
• How do you evaluate #g(b^2+1)# if #g(x)=(3-x)/(5+x)#?
• How do you evaluate #f(5m)# if #f(x)=abs(x^2-13)#?
• How do you write two functions for which #(f*g)(x)=2x^2+11x-6#?
• Given #f(x)=3x^2+4x-5# and #g(x)=2x+9#, how do you find #f(x)+g(x)#, #f(x)-g(x)# and #f(x)*g(x)# and #(f/g)(x)#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=2x+5# and #g(x)=3+x#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=2x-3# and #g(x)=x^2-2x#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=x^2-9# and #g(x)=x+4#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=1/2x-7# and #g(x)=x+6#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=x-4# and #g(x)=3x^2#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=x^2-1# and #g(x)=5x^2#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=2x# and #g(x)=x^3+x^2+1#?
• How do you find #[fog](x)# and #[gof](x)# given #f(x)=1+x# and #g(x)=x^2+5x+6#?
• How do you find #f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)# given #f(x)=x^2-2x# and #g(x)=x+9#?
• How do you find #f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)# given #f(x)=3/(x-7)# and #g(x)=x^2+5x#?
• How do you find #f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)# given #f(x)=x+3# and #g(x)=(2x)/(x-5)#?
• How do you find the domain of #[fog](x)# given #f(x)=5x# and #g(x)=x^3#?
• How do you find the domain of #[fog](x)# given #f(x)=1/x# and #g(x)=7-x#?
• How do you find the domain of #[fog](x)# given #f(x)=sqrt(x-2)# and #g(x)=1/(4x)#?
• How do you find #f(n-1)# if #f(x)=2x^2-x+9#?
• How do you find (f og)(x) and (g of)(x) given #f(x)=9x-5# and #g(x)=9-3x#?
• If f(x) = 2x + 1 and g(f(x)) = 4x^2 + 4x + 3 , find g(x), given that g(x) is in the form of ax^2 + bx + c. How?
• If #g(0) = 0#, #f'(0) = 2#, #f(0) = 4# and #g'(0) = 3#, then what is the value of #(f @ g)'(0)#?
• For #f(x)= x -3# and #g(x)= x^ 2+4#, how do you find f(g(x)) and g(f(x)) and state the range?
• How do you find the inverse of #y=x^2+12x#?
• Question #90e8c
• How do you find the inverse of #f(x)=4x +7#?
• How do you find the inverse of each of #y=2x-5# and graph them. Draw and label the line of symmetry for the inverse and the original graph?
• Given #f(x)=3x-1, g(x)=x^2-7, h(x)=x^4#, how do you find #(fog)(3)#?
• Given #f(x)=3x-1, g(x)=x^2-7, h(x)=x^4#, how do you find #(goh)(x)#?
• Given #f(x)=3x-1, g(x)=x^2-7, h(x)=x^4#, how do you find #f(g(h(x))#?
• Is the statement true: the graph of #f^-1# is obtained by reflecting the graph of the function f about the line y=x?
• How do you find the inverse of #f(x)=(x-4)/(33-x)#?
• What is the inverse of the function #f(x)=19/x^3#?
• If #f(x)=2x-5# and #g(x)=x^2+1#, what is g(f(x))?
• Let #f(x)=x^2# and #g(x)=sqrtx#, how do you find the domain and rules of #(f*g)(x)#?
• Let #f(x)=x^2# and #g(x)=sqrtx#, how do you find the domain and rules of #(f/g)(x)#?
• Let #f(x)=x^2# and #g(x)=sqrtx#, how do you find the domain and rules of #(f@g)(x)#?
• How do you determine the equation for the inverse of the function #y=2/3x^5#?
• If #f(x)=2x^2- 4x -3# and #g(x)= 2x^2- 16# how do you find f(x)+ g(x)?
• If #f(x)=x^2-81# and #g(x)=(x-9)^-1(x+9)#, how do you find #g(x)timesf(x)#?
• How do you prove that f(x) and g(x) are inverses of each other?
• For #f(x)=x/(x+1)# and #g(x)=9/x#, how do you find #(fog)(x)#?
• Given that f is even function and g is odd function, how do you determine whether h is even or odd or neither #h(x)=2f(x)+xg(x)#?
• How do you determine whether #f(x)=x^5-x# is even, odd, or neither?
• Given that #f(x)=sqrtx# and #g(x)=4x+2#, how do you find #(fog)(x)#?
• Given that #f(x)=sqrtx# and #g(x)=4x+2#, how do you find #(gof)(x)#?
• If #g(x)=2x+1#, how do you find #g(g(x))#?
• How do you find #(fog)(x)# given #f(x)=x^2+3; g(x)=6x#?
• How do you find #f(g(4))# given #f(x)=(x-2)^2; g(x)=x+3#?
• How do you find the inverse of #f(x)=6x#?
• How do you find the inverse of #f(x)=1/3x#?
• How do you find the inverse of #f(x)=3x+1#?
• How do you find the inverse of #f(x)=(x-1)/5#?
• How do you find the inverse of #f(x)=root3x#?
• How do you find the inverse of #f(x)=x^5#?
• How do you show that #f(x)=2x# and #g(x)=x/2# are inverse functions algebraically and graphically?
• How do you show that #f(x)=x-5# and #g(x)=x+5# are inverse functions algebraically and graphically?
• How do you show that #f(x)=7x+1# and #g(x)=(x-1)/7# are inverse functions algebraically and graphically?
• How do you show that #f(x)=3-4x# and #g(x)=(3-x)/4# are inverse functions algebraically and graphically?
• How do you show that #f(x)=x^3/8# and #g(x)=root3(8x)# are inverse functions algebraically and graphically?
• How do you show that #f(x)=1/x# and #g(x)=1/x# are inverse functions algebraically and graphically?
• How do you show that #f(x)=sqrt(x-4)# and #g(x)=x^2+4# are inverse functions algebraically and graphically?
• How do you show that #f(x)=1-x^3# and #g(x)=root3(1-x)# are inverse functions algebraically and graphically?
• How do you show that #f(x)=9-x^2# and #g(x)=sqrt(9-x)# are inverse functions algebraically and graphically?
• How do you show that #f(x)=1/(1+x)# and #g(x)=(1-x)/x# are inverse functions algebraically and graphically?
• How do you show that #f(x)=(x-1)/(x+5)# and #g(x)=-(5x+1)/(x-1)# are inverse functions algebraically and graphically?
• How do you show that #f(x)=(x+3)/(x-2)# and #g(x)=(2x+3)/(x-1)# are inverse functions algebraically and graphically?
• How do you use the horizontal line test to determine whether the function #g(x)=(4-x)/6# is one to one?
• How do you use the horizontal line test to determine whether the function #g(x)=10# is one to one?
• How do you use the horizontal line test to determine whether the function #g(x)=abs(x+4)-abs(x-4)# is one to one?
• How do you use the horizontal line test to determine whether the function #g(x)=(x+5)^3# is one to one?
• How do you use the horizontal line test to determine whether the function #f(x)=1/8(x+2)^2-1# is one to one?
• How do you find the inverse of #f(x)=2x-3# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=3x+1# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=x^5-2# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=x^3+1# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=sqrtx# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=x^2# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=x^2-2# from #x<=0# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=4/x# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=-2/x# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=(x+1)/(x-2)# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=(x-3)/(x+2)# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=root3(x-1)# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=x^(3/5)# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=(6x+4)/(4x+5)# and graph both f and #f^-1#?
• How do you find the inverse of #f(x)=(8x-4)/(2x+6)# and graph both f and #f^-1#?
• How do you determine whether the function #f(x)=x^4# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #f(x)=1/x^2# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #g(x)=x/8# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #f(x)=3x+5# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #p(x)=-4# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #f(x)=(3x+4)/5# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #q(x)=(x-5)^2# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #h(x)=-4/x^2# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #f(x)=sqrt(2x+3)# has an inverse and if it does, how do you find the inverse function?
• How do you determine whether the function #f(x)=sqrt(x-2)# has an inverse and if it does, how do you find the inverse function?
• Given #f(x)=1/8x-3# and #g(x)=x^3#, how do you find #(f^-1og^-1)(1)#?
• Given #f(x)=1/8x-3# and #g(x)=x^3#, how do you find #(g^-1of^-1)(-3)#?
• Given #f(x)=1/8x-3# and #g(x)=x^3#, how do you find #(f^-1of^-1)(6)#?
• Given #f(x)=1/8x-3# and #g(x)=x^3#, how do you find #(g^-1og^-1)(-4)#?
• Given #f(x)=1/8x-3# and #g(x)=x^3#, how do you find #(fog)^-1#?
• If #f(x)=x^(1/2)-x# and #g(x)=2x^3-x^(1/2)-x#, how do you find #f(x)-g(x)#?
• How do you find #h(x)=f(x)+g(x)# given #f(x)=abs(x-3)# and #g(x)=4#?
• How do you find #h(x)=f(x)+g(x)# given #f(x)=3x-5# and #g(x)=-x+2#?
• How do you find #h(x)=f(x)+g(x)# given #f(x)=-x-5# and #g(x)=(x+3)^2#?
• How do you find #h(x)=f(x)-g(x)# given #f(x)=6x# and #g(x)=x-2#?
• How do you find #h(x)=f(x)-g(x)# given #f(x)=6-x# and #g(x)=(x+1)^2-2#?
• How do you find #h(x)=f(x)-g(x)# given #f(x)=cosx# and #g(x)=4#?
• Given #f(x)=3x^2+2, g(x)=sqrt(x+4), h(x)=4x-2# how do you determine the combined function #y=(h-g)(x)# and state its function?
• Given #f(x)=3x^2+2, g(x)=sqrt(x+4), h(x)=4x-2# how do you determine the combined function #y=(g-h)(x)# and state its function?
• Given #f(x)=2^x, g(x)=4# how do you determine the combined function #y=(f-g)(x)# and state its function?
• Given #f(x)=3x^2+2, g(x)=4x, h(x)=7x-1#, how do you determine the combined function of #y=f(x)+g(x)+h(x)#?
• Given #f(x)=3x^2+2, g(x)=4x, h(x)=7x-1#, how do you determine the combined function of #y=f(x)+g(x)-h(x)#?
• Given #f(x)=3x^2+2, g(x)=4x, h(x)=7x-1#, how do you determine the combined function of #y=f(x)-g(x)+h(x)#?
• Given #f(x)=3x^2+2, g(x)=4x, h(x)=7x-1#, how do you determine the combined function of #y=f(x)-g(x)-h(x)#?
• If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=x^2+5x+2#?
• If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=sqrt(x+7)+5x+2#?
• If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=2x+3#?
• If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=3x^2+4x-2#?
• If #h(x)=(f-g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=-x^2+5x+3#?
• If #h(x)=(f-g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=sqrt(x-4)+5x+2#?
• If #h(x)=(f-g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=-3x+11#?
• How do you determine #h(x)=f(x)g(x)# and #k(x)=f(x)/g(x)# given #f(x)=x+7# and #g(x)=x-7#?
• How do you determine #h(x)=f(x)g(x)# and #k(x)=f(x)/g(x)# given #f(x)=2x-1# and #g(x)=3x+4#?
• How do you determine #h(x)=f(x)g(x)# and #k(x)=f(x)/g(x)# given #f(x)=sqrt(x+5)# and #g(x)=x+2#?
• How do you determine #h(x)=f(x)g(x)# and #k(x)=f(x)/g(x)# given #f(x)=sqrt(x-1)# and #g(x)=sqrt(6-x)#?
• Given #f(x)=x+2, g(x)=x-3, h(x)=x+4# how do you determine #y=f(x)g(x)h(x)#?
• Given #f(x)=x+2, g(x)=x-3, h(x)=x+4# how do you determine #y=(f(x)g(x))/(h(x))#?
• Given #f(x)=x+2, g(x)=x-3, h(x)=x+4# how do you determine #y=(f(x)+g(x))/(h(x))#?
• Given #f(x)=x+2, g(x)=x-3, h(x)=x+4# how do you determine #y=(f(x))/(h(x))times(g(x))/(h(x))#?
• If #h(x)=f(x)g(x)# and #f(x)=2x+5#, how do you determine g(x) given #h(x)=6x+15#?
• If #h(x)=f(x)g(x)# and #f(x)=2x+5#, how do you determine g(x) given #h(x)=-2x^2-5x#?
• If #h(x)=f(x)g(x)# and #f(x)=2x+5#, how do you determine g(x) given #h(x)=2xsqrtx+5sqrtx#?
• If #h(x)=(f(x))/(g(x))# and #f(x)=3x-1#, how do you determine g(x) given #h(x)=(3x-1)/(x+7)#?
• If #h(x)=(f(x))/(g(x))# and #f(x)=3x-1#, how do you determine g(x) given #h(x)=(3x-1)/sqrt(x+6)#?
• If #h(x)=(f(x))/(g(x))# and #f(x)=3x-1#, how do you determine g(x) given #h(x)=1/(x+9)#?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate f(g(3))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate f(g(2))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate g(f(2))?
• Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate g(f(3))?
• If #f(x)=2x+8# and #g(x)=3x-2#, how do you find #f(g(1))#?
• If #f(x)=2x+8# and #g(x)=3x-2#, how do you find #f(g(-2))#?
• If #f(x)=2x+8# and #g(x)=3x-2#, how do you find #g(f(-4))#?
• If #f(x)=2x+8# and #g(x)=3x-2#, how do you find #g(f(1))#?
• If #f(x)=3x+4# and #g(x)=x^2-1#, how do you find #f(g(a))#?
• If #f(x)=3x+4# and #g(x)=x^2-1#, how do you find #f(g(x))#?
• If #f(x)=3x+4# and #g(x)=x^2-1#, how do you find #g(f(x))#?
• If #f(x)=3x+4# and #g(x)=x^2-1#, how do you find #g(g(x))#?
• How do you determine #f(g(x))# and #g(g(x))#, given #f(x)=x^2+x# and #g(x)=x^2+x#?
• How do you determine #f(g(x))# and #g(g(x))#, given #f(x)=sqrt(x^2+2)# and #g(x)=x^2#?
• How do you determine #f(g(x))# and #g(g(x))#, given #f(x)=absx# and #g(x)=x^2#?
• Given #f(x)=sqrtx# and #g(x)=x-1#, how do you determine the domain and range of #y=f(g(x))#?
• If #h(x)=(fog)(x)#, how do you determine #h(x)=(2x-5)^2# and #f(x)=x^2#?
• Let #j(x)=x^2# and #k(x)=x^3#, does #k(j(x))=j(k(x))#?
• If #s(x)=x^2+1# and #t(x)=x-3#, does #s(t(x))=t(s(x))#?
• If #h(x)=f(g(x))# how do you determine f(x) and g(x) given #h(x)=2x^2-1#?
• If #h(x)=f(g(x))# how do you determine f(x) and g(x) given #h(x)=abs(x^2-4x+5)#?
• If #f(x)=1/(1+x)# and #g(x)=1/(2+x)# how do you determine f(g(x))?
• Let #f(x)=(x+3)^2# and #g(x)=x+4#, how do you find #h(x)=f(x)+g(x)#?
• Let #f(x)=x+8# and #g(x)=2x^2-128#, how do you find #h(x)=(g(x))/(f(x))#?
• Given #f(x)=5-x# and #g(x)=2sqrt(3x)# what is the value of #f(g(3))#?
• What is #y=f(g(x))# if #f(x)=x+5# and #g(x)=x^2#?
• What is #y=f(g(x))# if #f(x)=4^x# and #g(x)=x+1#?
• What is #y=f(g(x))# if #f(x)=x^4# and #g(x)=sqrtx#?
• Given #f(x)=2x^2+11x-21# and #g(x)=2x-3# how do you determine #y=f(x)-g(x)#?
• Given #f(x)=2x^2+11x-21# and #g(x)=2x-3# how do you determine #y=(f(x))/(g(x))#?
• Given #f(x)=2x^2+11x-21# and #g(x)=2x-3# how do you determine #y=f(g(x))#?
• Question #7ca7c
• Question #dfc1c
• How do you find the inverse of the function #f(x)=1/2x+10#?
• Question #37dc6
• Question #9ff05
• If #h(x)=2x-6# and #h(g(x))=2-2x#, find #g(x)#?
• Question #9e4a8
• Question #7adc3
• How do you find the equation for the inverse of #y=2x+1#?
• How do you find the equation for the inverse of #y=1/3x#?
• How do you find the equation for the inverse of #y=6x-3#?
• How do you find the equation for the inverse of #y=-4x+6#?
• How do you find the equation for the inverse of #y=x^2+2, x>=0#?
• How do you verify if #f(x)=x+4; g(x)=x-4# are inverse functions?
• How do you verify if #f(x)=7x; g(x)=1/7x# are inverse functions?
• How do you verify if #f(x)=x^5; g(x)root5x# are inverse functions?
• How do you verify if #f(x)=2x-4; g(x)=1/2x+2# are inverse functions?
• How do you verify if #f(x)=3-x; g(x)=3-x# are inverse functions?
• How do you verify if #f(x)=x^2+5; x>=0; g(x)=sqrt(x-5)# are inverse functions?
• How do you graph #f(x)=2x+1# and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph #f(x)=-x-2# and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph #f(x)=-x^2+3, x>=0# and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph #f(x)=1/4x^3# and then use the horizontal test to determine whether the inverse of f is a function?
• How do you graph #f(x)=3/x# and then use the horizontal test to determine whether the inverse of f is a function?
• How do you verify that #f(x)=3x+5; g(x)=1/3x-5/3# are inverses?
• How do you verify that #f(x)=-2x-3; g(x)=-1/2x-3/2# are inverses?
• How do you verify that #f(x)=x^2+2, x>=0; g(x)=sqrt(x-2)# are inverses?
• How do you verify that #f(x)=1/3x^3-2; g(x)=root3(3x+6)# are inverses?
• How do you verify that #f(x)=3x^4+1, x>=0; g(x)=root4(1/3x-1/3)# are inverses?
• How do you verify that #f(x)=(3-x)/x; g(x)=3/(x+1)# are inverses?
• How do you find the inverse of #f(x)=3-2x#?
• How do you find the inverse of #f(x)=1/5x+3#?
• How do you find the inverse of #f(x)=sqrt(x-3)#?
• How do you find the inverse of #f(x)=sqrt(2x+5)#?
• How do you find the inverse of #f(x)=4x^7#?
• How do you find the inverse of #f(x)=4x^2+1, x>=0#?
• How do you find the inverse of #f(x)=(4-x)/(3x)#?
• How do you find the inverse of #f(x)=root5(5x+4)#?
• How do you find the inverse of #f(x)=1/(2x)#?
• How do you graph the function #f(x)=-x^3+1# and then use the horizontal line test to determine whether the inverse of f is function?
• How do you graph the function #f(x)=(x+3)(x-1)# and then use the horizontal line test to determine whether the inverse of f is function?
• Relationship of Input and Output values of Composite Functions. How would you evaluate f(g(x)?
• What is the inverse function of #f(x) = 2log_4 x#?
• How do you solve this function? When x=(a+2).
• Question #d780a
• Question #da9aa
• If #f(x)=sqrtx#, #g(x)=7x+b# and #f(g(x))# passes through #(4,6)#, what is #b#?
• (k o h)? #k(x) = 1/x, h(x) = x^2 + 1# Find the indicated functions.
• (k o g)? k(x) = 1/x, g(x) = 2x^2 + 4x Find the indicated functions.
• Question #86e50
• Question #43f3b
• Question #55f42
• Let #f(x)=x^2+5# and #g(x)= (x+5)/x#. What is #(g*f)(-3)#?
• If #f(x) = sqrt(x+8)# and #g(x) = sqrt(x+7)#, what is #(f+g)(x)#?
• Find the function composition # f@g(x)=f(g(x))# where # f(x ) = 8x-18 # and # g(x) = 1/2x-1 #?
• Given that #f(x)=x+2# and #g( f(x) ) = x^2 + 4x-2# then write down #g(f(x))#?
• What is the composition form f(g(x)) for the following Chain Rule function, where the inner function u=g(x), and the outside y = f(u)?
• Let f(x)=#x^2+2# and g(x)=2x−2, evaluate: f(g(3))?
• Let f(x) = 2x − 5and g(x) = 5x − 2. what is (g ∘ f)(−6)?
• Let f(x) = 2x − 3and g(x) = 3x − 2. what is (f ∘ g)(−2)?
• Let f(x) = x2 − 9 and g(x) = 3x − 4. what is (f · g)(−3)?