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All monotonic mappings such that f(t)+f^{-1}(t)=2t

Source: IMO LongList 1979 - P21

June 1, 2011
floor functionfunctionalgebra proposedalgebra

Problem Statement

Let EE be the set of all bijective mappings from R\mathbb R to R\mathbb R satisfying f(t)+f−1(t)=2t,∀t∈R,f(t) + f^{-1}(t) = 2t, \qquad \forall t \in \mathbb R, where f−1f^{-1} is the mapping inverse to ff. Find all elements of EE that are monotonic mappings.
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