MathDB

Functions f:R+ to R satisfying f(xf(x)+yf(y))=xy

Source:

November 22, 2017

functionfunctional equationalgebraFunctional Equations

Problem Statement

Does there exist any function

f: \mathbb{R}^+ \to \mathbb{R}

such that for every positive real number

x,y

the following is true :

f(xf(x)+yf(y)) = xy