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Unexpectedly easy functional equation

Source: Mongolian Mathematical Olympiad 2024 P3

April 12, 2024
functional equationfunctionalgebra

Problem Statement

Let R+\mathbb{R}^+ denote the set of positive real numbers. Determine all functions f:R+ā†’R+f: \mathbb{R}^+ \to \mathbb{R}^+ such that for all positive real numbers xx and yy : f(x)f(y+f(x))=f(1+xy)f(x)f(y+f(x))=f(1+xy)
Proposed by Otgonbayar Uuye.
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