The long drawn method would be to susbtitute (1-x) for all values of x in each of the given equations and to see if we get the original equation f(x), as has already been shown by Anurag@Gurome.
However, to save time on expanding each equation in its multiples, one can just allocate a value for x. Lets say x = 0, then quickly substituting the same for the values of x, we shall have:
a) f(x) = 1-x = 1-0 = 1; f(1-x) = 1-(1-0)= 0 , therefore False.
b) f(x) = 1-x^2 = 1-0 = 1; f(1-x) = 1 - (1-0)^2= 1-1 = 0, therefore False
c) f(x) = x^2-(1-x)^2 = 0-1 = -1 ; f(1-x) = (1-0)^2 - (1-(1-0))^2 = +1, therefore False
d) f(x) = x^2(1-x)^2 = (0)^2(1)^2 = 0; f(1-x) = (1-x)^2(1-(1-x))^2 = 1^2(0)^2 = 0, therefore True.
e) f(x) = x/(1-x) = 0/1 = 0; f(1-x) = (1-x)/(1-(1-x)) = 1/0 = Infinity, therefore False.
I believe this method of substituting random (but simple) values for x will help in getting the solution faster, since time is a definite constraint in the GMAT exam. The other method of expanding each equation, is however, the most fool-proof method.
