If F:R>R and g:R>R defined by f(x)=2x+1 and g(x)=2^x find the equation for (gof) and (fog)?

Also find f^(-1)(x) and g(3)?

1 Answer
Ratnesh Bhosale
Jun 9, 2018

#gof(x)= 2^(2x+1)#
# fog(x) =2*2^x+1#
#f^-1(x)=(x-1)/2#
#g(3)=8#

Explanation:

It should be cleared that,
#gof(x)= g(f(x))# and# fog(x) =f(g(x))#
Given-
#f(x)=2x+1# and #g(x)=2^x#

  1. #gof(x):#
    #gof(x)= g(f(x))#
    #:.##gof(x)= g(2x+1)#
    #:.##gof(x)= 2^(2x+1)#
  2. # fog(x) :#
    #:.## fog(x) =f(2^x)#
    #:.## fog(x) =2*2^x+1#
  3. #f^-1(x):#
    Let , #y= 2x+1#
    #=># #x=(y-1)/2#
    Hence, #f^-1(x)=(x-1)/2#
  4. #g(3):#
    #g(x)=2^x#
    #g(3)=2^3#
    #g(3)=8#
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