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Source: 2019 MEMO Problem I-1

August 28, 2019
algebrafunctional equationmemoMEMO 2019injective function

Problem Statement

Find all functions f:Rā†’Rf:\mathbb{R} \to \mathbb{R} such that for any two real numbers x,yx,y holds f(xf(y)+2y)=f(xy)+xf(y)+f(f(y)).f(xf(y)+2y)=f(xy)+xf(y)+f(f(y)).
Proposed by Patrik Bak, Slovakia
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