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Romania NMO 2022 Grade 11 P1

Source: Romania National Olympiad 2022

April 20, 2022
calculusromaniafunction

Problem Statement

Let f:[0,1]→(0,1)f:[0,1]\to(0,1) be a surjective function.
[*]Prove that ff has at least one point of discontinuity. [*]Given that ff admits a limit in any point of the interval [0,1],[0,1], show that is has at least two points of discontinuity. Mihai Piticari and Sorin Rădulescu
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