If #f(x/(x+1))=(x-1)^2#, what is #f(3)#?

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Answer 1 · 2018-06-04T18:40:58

#25/4=6.25#.

Given that, #f(x/(x+1))=(x-1)^2#.

We require the value of #f(3)#.

Clearly the corresponding #x# for this can be obtained by solving

#x/(x+1)=3#.

#:. x=3x+3#.

#:. -2x=3," giving, "x=-3/2#.

Subst.ing #x=-3/2# in the formula for #f#, we get,

# f((-3/2)/(-3/2+1))=f(-3/2-:-1/2)=f(3)=(-3/2-1)^2#.

# rArr f(3)=25/4=6.25#.

Enjoy Maths.!

Answer 2 · 2018-06-04T18:47:11

#f(3) = 25/4#

We are looking for what value of #x# gives

#x/(x+ 1) = 3#

Solve the equation:

#x = 3x + 3#

#-2x = 3#

#x =-3/2#

Now simply plug #x= -3/2# into the formula

#f(3) = (-3/2 - 1)^2 = 25/4#