IMO 1979 LL FRA21

Let E be the set of all bijective mappings from R to R satisfying

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IMO 1979 LL FRA21

Origin: FRA

Problem

Let E be the set of all bijective mappings from R to R satisfying (\forallt \inR) f(t) + f −1(t) = 2t, where f −1 is the mapping inverse to f. Find all elements of E that are monotonic mappings.