Please note that it's one of the house rules to search for keywords before posting. ALL GMATprep questions have been answered at least once on this forum. One such example:

https://www.beatthegmat.com/f-x-f-1-x-fu ... 13580.html

mzimmer wrote:Please help with this question:
For which of the following functions f is f(x)=f(1-x) fpr a;; x?

A. f(x)=1-x
B. f(x)=1-x^2
C. f(x)=x^2- (1-x)^2
D. f(x)=x^2(1-x)^2
E. f(x)= x/1-x

Thank you!!

In other words, let´s pick f(x) = 3 then f (1-x)= -2

Plug in 3 and -2 in the answer choices to know whether you have the same results.

Ej. A) f(x) = 1-x Plug 3 f(3)= -2 Then Plug -2, f(-2)=F (1--2) =-1.Different results so this is not the answer.

Ej. D) f (3)= 9.4= 36 then f(-2)= 4. (-3)^2=36 Same answer in the two calculations, so this is correct.