MathDB

Estonian Math Competitions 2005/2006

Source: Seniors Problem 7

July 30, 2008

functionalgebra unsolvedalgebra

Problem Statement

A real-valued function

f

satisfies for all reals

x

and

y

the equality f (xy) \equal{} f (x)y \plus{} x f (y). Prove that this function satisfies for all reals

x

and

y \ne 0

the equality f\left(\frac{x}{y}\right)\equal{}\frac{f (x)y \minus{} x f (y)}{y^2}