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x <= y => f(x) <= f(y) , f(f(x)) = x

Source: Netherlands - Dutch NMO 1972 p2

January 27, 2023
functionalinequalitiesfunctional equationFunctional inequalityalgebra

Problem Statement

Prove that there exists exactly one function ƒƒ which is defined for all x∈Rx \in R, and for which holds: ∙\bullet x≤y⇒f(x)≤f(y)x \le y \Rightarrow f(x) \le f(y), for all x,y∈Rx, y \in R, and ∙\bullet f(f(x))=xf(f(x)) = x, for all x∈Rx \in R.
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