MathNet 2026 — Part 03 Question 99

Let $\mathbb{R}^{+}$ be the set of positive real numbers. Find all the functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$, such as $f(x+f(y))=y f(x y+1)$, for all $x, y\gt 0$.