MathDB

1

Part of 2022 Brazil Undergrad MO

Problems(1)

Functional analysis

Source: Brazilian Undergrad Mathematics Olympiad 2022 P1

11/23/2022
Let 0<a<10<a<1. Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} continuous at x=0x = 0 such that f(x)+f(ax)=x, ∀x∈Rf(x) + f(ax) = x,\, \forall x \in \mathbb{R}
functionFunctional Analysiscalculus