One last one from the practice CAT

I think the answer is (d) x^2(1-x)^2.

Replace the x in the equation to (1-x) and we will still get x^2(1-x)^2 = f(x)

Also another vote for d.

I picked an easy number x=1. So you have two functions to try out:

f(x) => f(1)
f(x-1) => f(1-1) = f(0)

so you have to see which of the answer choices are f(1) = f(0).

If you go through the equations in the selection and plug in both 1 and 0 for, you'll find choice d) is the only one that is equal to each other.

f(x) = x^2(1-x)^2
f(0) = 0^2(1-0)^2 = 0
f(1) = 1^2(1-1)^2 = 0

I'd think this may not be the quickest way, but it's the method that worked for me...