SOLUTION: Dear tutors, Please explain how to solve these kind of functions. 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 (x s

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Question 32437: Dear tutors,
Please explain how to solve these kind of functions.
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 (x squared)
c. f(x) = x^2 – (1-x)^2
d. f(x) = x^2(1-x)^2
e. f(x) = x/( 1-x)

by the way, this question is from a paper test i bought online.
Regards,
Tolly
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
a. f(x) = 1-x
b. f(x) = 1-x^2 (x squared)
c. f(x) = x^2 – (1-x)^2
d. f(x) = x^2(1-x)^2
e. f(x) = x/( 1-x)
I SHALL SHOW YOU ONE EXAMPLE ..YOU TRY THE REST.......
F(X-1)...MEANS PUT X-1 WHEREVER X WAS THERE IN F(X)..SO WE GET
A)...F(X)=1-X...
F(1-X)=1-(1-X)=1-1+X=X...COMPARE IT WITH F(X)...IF BOTH ARE SAME THEN ONLY YOU CAN SAY F(X)=F(1-X)..FOR ALL X...
HERE F(X)=1-X AND F(1-X)=X..HENCE THEY ARE NOT SAME..NO IS THE ANSWER..