KöMaL problem A, 2018

Algebra Difficulty 7.0 National Olympiad, round 2 Find the answer Hungary

Let $\mathbb{R}^+$ denote the set of positive real numbers. Find all functions $f\colon \mathbb{R}^+\to \mathbb{R}^+$ satisfying the following equation for all $x,y\in\mathbb{R}^+$ :

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