IMO 2022 Problem 2
Working
Proposed by: -
Verified: no
Verdicts: UNKNOWN + UNKNOWN
Solve time: 43s
Problem
Let $\mathbb{R}^+$ denote the set of positive real numbers. Find all functions $f : \mathbb{R}^+ \to \mathbb{R}^+$ such that for each $x \in \mathbb{R}^+$, there is exactly one $y \in \mathbb{R}^+$ satisfying
$$ xf (y) + yf (x) \le 2 $$.
Working