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

by **Abdulla** Sun Nov 09, 2008 3:16 am

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)=x/1-x

The answer is D

Getting confused with this question.. I found solutions in another forums but non of them was clear.

by **jade3** Sun Nov 09, 2008 11:45 am

Replace (1-x) for x and you will get the answer

by **Abdulla** Sun Nov 09, 2008 8:26 pm

If I did A will be the answer..

f(1-x)= (1-(1-x)) = 0+x = x ... so what is next ?

by **Guest** Wed Nov 12, 2008 1:05 am

If f(x)=1-x and f(1-x)=1-(1-x)=x, then they are not the same. Thus, it's not the right answer.

I would pick number on this question.

x=3, 1-3=-2

A 1-3=-2, 1-(-2)=3 Not the same.

B. 1-(3)^2=-8, 1-(-2)^2=-3 Not the same.

C. 3^2-(1-3)^2= 9-4=5, (-2)^2-(1+2)^2=4-9=-5 Not the same

D. (3)^2(1-3)^2=9*4=36, (-2)^2(1+2)^2=4*9=36, Same answer.

E. (3)/(1-3)=-3/2, -2/(1+2)=-2/3, Not the same.

Eric

by **JonathanSchneider** Wed Nov 19, 2008 9:18 pm

Number picking would certainly work, but algeba will give you a universal right answer. So, if you're comfortable with algebra, use that. Otherwise, test numbers (but don't pick 1 or 0).

The trick here is to recognize that we need to plug in x and (x-1) separately into each of the functinos in the answer choices, to see where we get the same value. We do NOT want to simply plug in (x-1) and see where it = x. The question asks for something different from that.