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 32436: 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 mukhopadhyay(490) (Show Source):
You can put this solution on YOUR website!
f(x) = f(1-x) for all x
......................
a. f(x) = 1-x
=> f(1-x) = 1-(1-x) = x
f(x)=f(1-x) => x=1-x => x=1/2;
............
b. f(x) = 1-x^2
=> 1-x^2 = x^2 (using the same approach as above)
=> x^2 = 1/2 => x=1/sqrt(2) or x=-1/(sqrt(2);
.........................
c. f(x) = x^2 � (1-x)^2
=> x^2 - (1-x)^2 = (1-x)^2 - (x^2) (using the same approach as in a.)
=> x^2 = (1-x)^2
=> (x)(x) = 0
=> x=0
........................
d. f(x) = x^2(1-x)^2
=> x^2(1-x)^2 = (1-x)^2(x^2) (using the same approach as in a.)
The above is true for all real x => x is any real number
.............
e. f(x) = x/( 1-x)
=> x/(1-x) = (1-x)/x (using the same approach as in a.)
=> x^2 = (1-x)^2
=> x^2 = x^2-2x+1
=> x = 1/2