IMO 1992 LL MON48

Find all the functions f : R+ oR satisfying the identity

IMO 1992 LL MON48

Origin: MON

Problem

Find all the functions f : R+ \toR satisfying the identity f(x)f(y) = y\alpha \cdot f x

  • x\beta \cdot f y , x, y \inR+, where \alpha, \beta are given real numbers.