steinbock wrote: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)

OA is D

Please explain why this answer is correct. Thank you.

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Thanks

I tried to look for this but didn't find it. Thank you very much for your help

A. f(x)=1-x and f(x-1)= x hence, not equal

Tip: just substitue x as x-1 in the equation given for A


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

c. f(x)=x^2-(1-x)^2 and f(x-1)=-x^2 +(1-x)^2 hence, not equal



D- f(x)=x^2*(1-x)^2 and f(x) solves to be same

hence IMO D

Probably functions are the only area when u dont have to solve all unless you are calculations are correct and usally start from the end