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Slovenia 2019 TST2 P2

Source: 2019 Slovenia 2nd TST Problem 2

February 14, 2019
TSTFunctional Equationsalgebrafunctional equation

Problem Statement

Determine all non-negative real numbers aa, for which f(a)=0f(a)=0 for all functions f:R≥0→R≥0f: \mathbb{R}_{\ge 0}\to \mathbb{R}_{\ge 0} , who satisfy the equation f(f(x)+f(y))=yf(1+yf(x))f(f(x) + f(y)) = yf(1 + yf(x)) for all non-negative real numbers xx and yy.
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