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periodic wanted, g(x)=f(x+a), f even, g odd - 1989 Greece MO Grade XI p1

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September 7, 2024
algebraperiodic functionperiodic

Problem Statement

Consider two functions f, g :R→Rf , \,g \,:\mathbb{R} \to \mathbb{R} such that from some a>0a>0 holds g(x)=f(x+a)g(x)=f(x+a) for any x∈Rx \in \mathbb{R}. If ff is even and gg is odd, prove that both functions are periodic.
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