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Another simple functional equation

Source: 2020 Taiwan TST Round 2 Independent study 2-1

May 23, 2020
functionalgebrafunctional equationTaiwan

Problem Statement

Let R\mathbb{R} denote the set of all real numbers. Determine all functions f:Rā†’Rf:\mathbb{R}\to\mathbb{R} such that for all real numbers xx and yy, f(xy+xf(x))=f(x)(f(x)+f(y)).f(xy+xf(x))=f(x)\left(f(x)+f(y)\right).
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