Problem

Source: 2015 Saudi Arabia IMO TST I p1

Tags: algebra, functional, functional equation



Find all functions $f : R_{>0} \to R$ such that $f \left(\frac{x}{y}\right) = f(x) + f(y) - f(x)f(y)$ for all $x, y \in R_{>0}$. Here, $R_{>0}$ denotes the set of all positive real numbers. Nguyễn Duy Thái Sơn