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

[jackiesong83]

For which of the folloiwng 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. f(x) = x/1-x

help.

[sarathsasikumar]

Answer is D f(x) = x^2(1-x)^2

Try replacing "x" with "1-x" in each of the options. In a, b,c and d you will find that f(x) is not equal to f(1-x).

But in D,

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

So, f(1-x) equals (1-x)^2 [1- (1-x)]^2 = (1-x)^2 x^2 which is the same as f(x).

Hence D

[RonPurewal]

there are already many, many posts on this problem. please search the forums before posting it yet again!

here's one:
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-t283.html