functions

[gmatguy81]

function

[iamseer]

answer 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)

[kevincanspain]

Iamseer's response proves that D is the correct answer.

Another way to approach this type of question is to reason that if the equation holds for all real values of x, it must do so for the simplest value of x, namely 0. Look for a function in which f(1-0) = f(0), i.e. f(1)=f(0)


Also, notice that 1- (1- x) = x : look for a function in which x and 1 - x are treated equally