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Positive real valued function with positive real inputs

Source: 4th Memorial Mathematical Competition "Aleksandar Blazhevski - Cane"- Junior D1 P3/ Senior D1 P2

December 20, 2022
algebrafunctionPositive realsinjectivitysurjectivityFixed point

Problem Statement

Let R+\mathbb{R}^{+} be the set of positive real numbers. Find all functions f:R+ā†’R+f:\mathbb{R}^{+} \rightarrow \mathbb{R}^{+} such that for all x,y>0x,y>0 we have
f(xy+f(x))=yf(x)+x.f(xy+f(x))=yf(x)+x.
Proposed by Nikola Velov
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