IMO 1987 LL BEL7

Origin: BEL

Problem

Let f : (0, +\infty) \toR be a function having the property that f(x) = f(1/x) for all x > 0. Prove that there exists a function u : [1, +\infty) \toR satisfying u  x+1/x = f(x) for all x > 0.