MathDB
f(x+y)f(f(x)-y)=xf(x)-yf(y)

Source: 2008 Japan Mathematical Olympiad Finals Problem 4

February 12, 2008
functionalgebra proposedalgebra

Problem Statement

Find all functions f:R→R f : \mathbb{R} \to \mathbb{R} such that f(x\plus{}y)f(f(x)\minus{}y)\equal{}xf(x)\minus{}yf(y) for all  x,y∈R. \ x,y \in \mathbb{R}.
Back to ProblemsView on AoPS