MathDB

Function problem

Source: Azerbaijan Math Olympiad Training

December 15, 2019

algebrafunctional equationTST

Problem Statement

Find all functions

u:R\rightarrow{R}

for which there exists a strictly monotonic function

f:R\rightarrow{R}

such that

f(x+y)=f(x)u(y)+f(y)

for all

x,y\in{\mathbb{R}}