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Part of 2011 Romanian Master of Mathematics

Problems(1)

RMM2011, P 1, Day 1 - Find monotonous functions

Source:

Prove that there exist two functions

f,g \colon \mathbb{R} \to \mathbb{R}

f\circ g

is strictly decreasing and

g\circ f

is strictly increasing.
(Poland) Andrzej Komisarski and Marcin Kuczma

functionalgebra proposedalgebra