Problem

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Tags: function, algebra



Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that:$$f(\max \left\{ x, y \right\} + \min \left\{ f(x), f(y) \right\}) = x+y $$for all real $x,y \in \mathbb{R}$ Proposed by Nikola Velov