MathDB
f(x)+f(yf(x)+f(y))=f(x+2f(y))+xy

Source: 8th European Mathematical Cup, Senior Category, Q4

December 26, 2019
functional equationalgebra

Problem Statement

Find all functions f:R→Rf:\mathbb{R}\to \mathbb{R} such that f(x)+f(yf(x)+f(y))=f(x+2f(y))+xyf(x)+f(yf(x)+f(y))=f(x+2f(y))+xyfor all x,y∈Rx,y\in \mathbb{R}.
Proposed by Adrian Beker
Back to ProblemsView on AoPS