INMO 1994 Problem 6

Find all real-valued functions $f$ on the reals such that $f(-x) = -f(x)$ , $f(x+1) = f(x) + 1$ for all $x$ , and $f\left(\dfrac{1}{x}\right) = \dfrac{f(x)}{x^2}$ for $x \not = 0$ .