Problem Solving

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

Thanks so much!

i used numbers

if i use x = 3 then

f(3) = f(1-x) or f(3) = (-2)

then i go through each question by doing:

a) f(x) = (1-x)
(1-3) = (1-(-2))
(-2) = (3) so this is wrong

i work may way down until d comes up
f(x) = x^2(1-x)^2

3^2(1-3)^2 = -2^2(1-(-2))^2
9(4) = 4(9)

this should work for any number you choose

so answer is D

thank you! functions has always been a weakness of mine! =) but just to make sure....this is what you did right??

set x=3 and plug it into the given function f(x)=f(1-x) which gives you:
f(3)=f(-2)

and then for all the answer choices you plugged in x=3 on one side and x=-2 for the other side and see which one is equal??

that is correct..try for any number x