olymmath

NMC 2022 Problem 1

  • Answer

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} such that

f(f(x)f(1−x))=f(x) and f(f(x))=1−f(x)f(f(x) f(1-x))=f(x) \text { and } f(f(x))=1-f(x)

for all real xx.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=\frac{1}{2}

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