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Functional Equation

Source: 2015 Indonesia Math Olympiad Day 1 Problem 4

June 30, 2017
functionalgebrafunctional equation

Problem Statement

Let function pair f,g:R+→R+f,g : \mathbb{R^+} \rightarrow \mathbb{R^+} satisfies f(g(x)y+f(x))=(y+2015)f(x) f(g(x)y + f(x)) = (y+2015)f(x) for every x,y∈R+x,y \in \mathbb{R^+} a. Prove that f(x)=2015g(x)f(x) = 2015g(x) for every x∈R+x \in \mathbb{R^+} b. Give an example of function pair (f,g)(f,g) that satisfies the statement above and f(x),g(x)≥1f(x), g(x) \geq 1 for every x∈R+x \in \mathbb{R^+}
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