Problem

Source: Iran 3rd round 2014-Algebra exam-P2

Tags: function, induction, algebra proposed, algebra



Find all continuous function $f:\mathbb{R}^{\geq 0}\rightarrow \mathbb{R}^{\geq 0}$ such that : \[f(xf(y))+f(f(y)) = f(x)f(y)+2 \: \: \forall x,y\in \mathbb{R}^{\geq 0}\] Proposed by Mohammad Ahmadi