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A simple functional equation

Source: 2020 Taiwan TST Round 1 Mock Exam 2

May 23, 2020
functionalgebrafunctional equationTaiwan

Problem Statement

Let R\mathbb{R} be the set of all real numbers. Find all functions f:R→Rf:\mathbb{R}\to\mathbb{R} such that for any x,y∈Rx,y\in \mathbb{R}, there holds f(x+f(y))+f(xy)=yf(x)+f(y)+f(f(x)).f(x+f(y))+f(xy)=yf(x)+f(y)+f(f(x)).
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