hi moneyman, this question has tricked you! remember for a function:
f(x)= f(1-x) does NOT EQUAL f(x)=1-x

Notice the difference:
f(x)=1-x ----this is only 1 function
f(x)= f(1-x) -----this has 2 functions---2 fs...

ok lets proceed to how to solve this. you have to pick numbers. easy numbers. b/c when you look at the answer choices there is x^2 ....so if you pick large numbers, it will be timing consuming.

I picked x=3

f(x)=f(1-x)
f(3)=f(-2)

the only one that worked is D.

f(3)= (3^2)* (1-3)^2
=36

f(-2)= -2^2* (1+2)^2
=36

the other choices don't work b/c when you plug in f(3) and f(-2)...they don't equal.

Or you can do this with algebra. For f(x) = f(1-x) then whenever you put (1-x) for 'x' in the answer choices, you can manipulate it to be what f(x) is.

[A] f(1-x) = 1 - (1-x) = -x. Not equal to f(x)

f(1-x) = 1 - (1-x)^2 = -2x + x^2. Not equal to f(x)

[C] f(1-x) = (1-x)^2 - (1-(1-x))^2 = 1 - 2x +x^2 - x^2 = 1 - 2x. Not equal to f(x)

[D] f(1-x) = (1-x)^2 * (1-(1-x))^2 = (1-x)^2*x^2. This is exactly what f(x) equals and is the correct answer choice.

[E] f(1-x) = (1-x)/(1-(1-x)) = (1-x)/x. Not equal to f(x)

Hope this provides a different way to approach the problem.