MathDB

Functional analysis

Source: Brazilian Undergrad Mathematics Olympiad 2022 P1

November 23, 2022

functionFunctional Analysiscalculus

Problem Statement

Let

0<a<1

. Find all functions

f: \mathbb{R} \rightarrow \mathbb{R}

continuous at

x = 0

such that

f(x) + f(ax) = x,\, \forall x \in \mathbb{R}