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f(x + y) = f(x)g(y) + f(y), strictly increasing f

Source: 2012 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST)

October 3, 2020
algebrafunctional equationfunctional

Problem Statement

Find all functions g:R→Rg : R \to R, for which there exists a strictly increasing function f:R→Rf : R \to R such that f(x+y)=f(x)g(y)+f(y)f(x + y) = f(x)g(y) + f(y).
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