MathDB

Functional equation: f(xy)=max{f(x+y),f(x)f(y)}

Source: XVIII Olimpíada Matemática Rioplatense (2009)

July 23, 2011

functionalgebradomainalgebra unsolved

Problem Statement

Find all functions

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

such that

f(xy)=\max\{f(x+y),f(x) f(y)\}

for all real numbers

x

and

y