Let be a function continuous on and define

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let ff be a function continuous on R\mathbb{R} and define h(x)=⌈f(x)⌉h(x)=\lceil f(x) \rceil, where ⌈ ⋅ ⌉\lceil\,\cdot\,\rceil denotes the ceiling function. Describe precisely the set of points where hh is discontinuous.

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