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Almost strictly increasing functions

Source: RMO 2006

April 18, 2006
functionreal analysisreal analysis unsolved

Problem Statement

Let f:[0,∞)→Rf: [0,\infty)\to\mathbb R be a function such that for any x>0x>0 the sequence {f(nx)}n≥0\{f(nx)\}_{n\geq 0} is increasing. a) If the function is also continuous on [0,1][0,1] is it true that ff is increasing? b) The same question if the function is continuous on Q∩[0,∞)\mathbb Q \cap [0, \infty).
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