You have to make sure that F(x) = F(1-x). So chose a random X (let's use 1 for this example), and check tha value of the function for x=1 and the value of a function for x=1-x=1-1=0
So use 1 and 0 to check the values of each function from a through e and you will see that for D both equal 0

GhassanMBA wrote:I encountered this question on the GMAT Prep 1 practice test, i'm hoping someone can help me out:

For which of the following functions f is f(x) = f(1-x) for all x ?

A) f(x) = 1 - x

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

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

D) f(x) = x^2 * (1 - x )^2

E)

The OA is D



I'm having difficulty understanding what the question is asking exactly. Hope someone can clarify this.

Thanks

A ) f(x) = 1 - x
f(1-x) = 1- (1-x) = x
f(x) is not f(1-x) for all x

B) f (x) = 1-x^2 = (1+x) (1-x)
f(1-x) = (1+ (1-x))* (1- (1-x)
= x(2-x)
f(x) is not f(1-x) for all x

C) f(x) = x^2 - (1-x)^2
f(1-x) = (1-x)^2 - x^2
f(x) is not f(1-x) for all x

D)f(x) = x^2 * (1 - x )^2
f(1-x) = (1-x)^2 *(1-(1-x))^2
= (1-x)^2 * (x)^2

f(x) = f(1-x) for all x

E) f(x) = x / ( 1 - x )
f(1-x) = 1-x/(1-(1-x))
= (1-x)/x

f(x) is not f(1-x) for all