You could also approach this from a conceptual perspective. This sort of question bothers a lot of students because it doesn't define a function in the traditional way. On the typical GMAT question, I give you a function - say, f(x) = 3x + 5 - then ask you to do something with that function, such as determine the value of f(9), or whatever.
This question, on the other hand, doesn't define a function; it asks for a function that gives the same output for two different input values. Imagine a question like, "Give a function for which f(9) is equal to f(6)." One answer to that question would be f(x) = x^2 - 15x + 54, because f(6) = 0 and f(9) = 0, so f(6) = f(9).
Our question, of course, is more abstract than my example. It wants a function for which f(x) = f(1-x), a condition that can be tough to even understand at first. But once you get what it's asking for, the question isn't so bad: you just have to find a function for which f(x) = some number and f(1-x) = that same number. (D) is the right answer because f(x) = x^2 * (1-x)^2 and f(1-x) = (1-x)^2 * (1-(1-x))^2, which simplifies to (1-x)^2 * x^2, which is the same thing as f(x), only backwards.
This a great question, by the way: I've had students who ended up scoring 45-48 on the quant section who struggled with it multiple times (i.e. they missed it, got the explanation, then still missed it again a week or two later!), so it's a doozy.
