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Romania District Olympiad 2002 - Grade XI

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March 18, 2011
functionreal analysisreal analysis unsolved

Problem Statement

Consider a function f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} such that:
1. ff has one-side limits in any a∈Ra\in \mathbb{R} and f(a−0)≤f(a)≤f(a+0)f(a-0)\le f(a)\le f(a+0).
2. for any a,b∈R, a<ba,b\in \mathbb{R},\ a<b, we have f(a−0)<f(b−0)f(a-0)<f(b-0).
Prove that ff is strictly increasing.
Mihai Piticari & Sorin Radulescu
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