PP-T1-168

[max999]

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
Ans:D

[amyliang]

using original equaiton f (x) = f (1 - x) ,
f(1)=(f1-1)=f(0)
A f(1)=1-1=0, f(0)=1-0=1 that is to say, f(1)><f(0)
B f(1)=1-1^2=0, but f(0)=1-0=1 f(1)>< f(0)
do the same job until you find that f(1)=f(0)