MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions
Problem
Suppose f is continuous on R. Define g(x)=⌊f(x)⌋, where ⌊⋅⌋ denotes the greatest integer less than or equal to its argument. Which of the following best describes the possible types of discontinuities of g?
(a) g can have both jump and removable discontinuities.
(b) g can have only removable discontinuities.
(c) g can have only jump discontinuities.
(d) g remains continuous everywhere because f is continuous.