MathDB
Hard functional equation

Source: Brazil National Olympiad 2019 #3

November 14, 2019
functional equationalgebra

Problem Statement

Let R>0\mathbb{R}_{>0} be the set of the positive real numbers. Find all functions f:R>0→R>0f:\mathbb{R}_{>0} \rightarrow \mathbb{R}_{>0} such that f(xy+f(x))=f(f(x)f(y))+xf(xy+f(x))=f(f(x)f(y))+x for all positive real numbers xx and yy.
Back to ProblemsView on AoPS