functions

[gmatgirl12]

Which of the following functions f is f(x)=f(1-x) for all 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)

I wasn't even sure where or how to begin this problem. Any advice?

Thank you.

[CrackGMAC]

Its D. Very simple.

f(x)= x^2(1-x)^2
f(1-x)=(1-x)^2 x^2

Hence, f(x)=f(1-x) for all x

[mp2437]

This was solved in another thread, but in any case,
just try plugging in any number, i.e: x = 2.