VMO 2022 Problem 2

Find all function $f:\mathbb R^+ \rightarrow \mathbb R^+$ such that: $f\left(\frac{f(x)}{x}+y\right)=1+f(y), \forall x,y \in \mathbb R^+.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.