MathDB
Determine all functions

Source: 69 Polish MO 2018 Second Round - Problem 1

April 28, 2018
functional equationalgebraPolandfunction

Problem Statement

Determine all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} which satisfy conditions: f(x)+f(y)≥xyf(x) + f(y) \ge xy for all real x,yx, y and for each real xx exists real yy, such that f(x)+f(y)=xyf(x) + f(y) = xy.
Back to ProblemsView on AoPS