function from Korea

[orl]

Suppose that for any real x with |x| <> 1, a function f(x) satisfies f((x-3)/(x+1)) + f((x+3)/(x-1)) = x. Find all possible f(x).

[harazi]

This should be classical. Denote y=(x-3)/(x+1). So, f(y)+f((-3+y)/(1+y))=(3+y)/(1-y).Similarly, put z=(3+x)/(1-x) and find that f(z)+f((3+z)/(1-z))=(z-3)/(z+1). Put here z=y and add this to the previous one. Use also the relation in the problem and you will find that f(y)=(7y+y^3)/(2-2y^2). Again, I don't want to check that this is a solution.

[A1lqdSchool]

I Think the problem is not correct
Problem is :f((x-3)/(x+1))+f((3+x)/(1-x))=x

[harazi]

Yeah! But the solution is correct, since I solved your problem!