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Restriction of f to the set of irrationals is injective

Source: IMO LongList 1982 - P29

March 18, 2011
functionlimitalgebra unsolvedalgebra

Problem Statement

Let f:Rā†’Rf : \mathbb R \to \mathbb R be a continuous function. Suppose that the restriction of ff to the set of irrational numbers is injective. What can we say about ff? Answer the analogous question if ff is restricted to rationals.
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