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Continuous function

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

August 31, 2014
functioninductionalgebra proposedalgebra

Problem Statement

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