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f(x)^2=f(x sqrt(2))

Source: Brazilian Undergrad MO 2021 Problem 2

May 12, 2022
functionsreal analysisfunctionBrazilian Undergrad MO 2021

Problem Statement

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} from C2C^2 (id est, ff is twice differentiable and f′′f'' is continuous.) such that for every real number tt we have f(t)2=f(t2)f(t)^2=f(t \sqrt{2}).
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