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f(x+y) = f(x)u(y)+ f(y) , strictly increasing function f : R \to R

Source: Ukrainian TST 1999 p9

February 13, 2020
functionfunctional equationalgebra

Problem Statement

Find all functions u:R→Ru : R \to R for which there is a strictly increasing function f:R→Rf : R \to R such that f(x+y)=f(x)u(y)+f(y)f(x+y) = f(x)u(y)+ f(y) for all x,y∈Rx,y \in R.
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