How to attempt this problem?

[daon]

Found this on the net: http://math.colorado.edu/Problem%20of%2 ... /apr06.pdf

\(\displaystyle \text{Find all the functions f(x) defined for x } \neq 0 \text{ and x } \neq \text{1 s.t.} \\ \,\,\L f(x) + f(\frac{1}{1-x}) = x^2\)

I'm not really sure where to start with this. Any ideas?

 

[daon]

Hmm, I;ve been thinking... For this to be true, wouldn't this have to hold: for some k, l

\(\displaystyle \,\,\L f(x) = kx^2 \,\, \text{and} \,\, f(\frac{1}{1-x}) = lx^2 \text{ s.t. } k+l = 1\)

That's got to be wrong. What function can possibly map both x and 1/(1-x) to cx^2? I really have know idea what I'm doing, I've just been fumbling around with this...