MathDB

Functional equation

Source: Baltic Way 2016, Problem 8

November 5, 2016

algebrafunctional equation

Problem Statement

Find all real numbers

a

for which there exists a non-constant function

f :\Bbb R \to \Bbb R

satisfying the following two equations for all

x\in \Bbb R:

i)

f(ax) = a^2f(x)

and ii)

f(f(x)) = a f(x).

Back to Problems View on AoPS