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A neat FE on positive reals

Source: The Golden Digits Contest, February 2024, P1

April 8, 2024
algebrafunctional equation

Problem Statement

Determine all functions f:R+→R+f:\mathbb{R}_+\to\mathbb{R}_+ which satisfy f(yf(x))+x=f(xy)+f(f(x)),f\left(\frac{y}{f(x)}\right)+x=f(xy)+f(f(x)),for any positive real numbers xx and yy.
Proposed by Pavel Ciurea
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