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Source: Latvian TST for Baltic Way 2022 P3

October 25, 2022
functional equationTST

Problem Statement

Let R\mathbb R be the set of real numbers. Determine all functions f:R→Rf:\mathbb R\to\mathbb R that satisfy the equationf(f(x))+yf(xy+1)=f(x−f(y))+xf(y)2. f(f(x))+yf(xy+1) = f(x-f(y)) + xf(y)^2. for all real numbers xx and yy.
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