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All functions f such that f(1-x)=1-f(f(x))

Source: Iran Third Round MO 1997, Exam 1, P1

June 30, 2012
functionalgebra unsolvedalgebra

Problem Statement

Find all strictly ascending functions ff such that for all x∈Rx\in \mathbb R, f(1−x)=1−f(f(x)).f(1-x)=1-f(f(x)).
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