You could solve this problem algebraically. For each of the answer choices, substitute (1 - x) for every instance of (x) to find f(1 - x). Then simplify and see if the two are equal:
a. f(x)= 1-x
f(1 - x) = 1 - (1 - x), so f(1 - x) = x --> not equal
b. f(x)= 1-x²
f(1 - x)= 1 - (1 - x)², so f(1 - x) = 2x - x² --> not equal
c. f(x)= x² - (1 - x)² , so f(x) = 2x - 1
f(1 - x)= x² - (1 - (1 - x))², so f(1 - x) = 0 --> not equal
d. f(x)= x²(1-x)² , so f(x) = x²(1 - 2x + x²)
f(1 - x)= (1 - x)²(1 - (1 - x))², so f(1 - x) = (1 - 2x + x²)(x²) --> equal!
e. f(x)= x/(1-x)
f(1 - x)= x/(1 - (1 - x)) , so f(1 - x) = 1 --> not equal
However, this is a MUCH more time-consuming approach. Picking numbers as Mitch did is a much better way to solve. Personally, I'd always pick 1 or 0, as those often are easier to calculate, but it doesn't make much difference.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
