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RMM2011, P 1, Day 1 - Find monotonous functions

Source:

February 25, 2011
functionalgebra proposedalgebra

Problem Statement

Prove that there exist two functions f,g ⁣:R→Rf,g \colon \mathbb{R} \to \mathbb{R}, such that f∘gf\circ g is strictly decreasing and g∘fg\circ f is strictly increasing.
(Poland) Andrzej Komisarski and Marcin Kuczma
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