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Romania District Olympiad 2011 - Grade XI

Source:

March 12, 2011
functionanalytic geometrygraphing linesslopeinequalitiestriangle inequalityreal analysis

Problem Statement

Find all the functions f:[0,1]→Rf:[0,1]\rightarrow \mathbb{R} for which we have:
∣x−y∣2≤∣f(x)−f(y)∣≤∣x−y∣,|x-y|^2\le |f(x)-f(y)|\le |x-y|,
for all x,y∈[0,1]x,y\in [0,1].
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