Question

Show that the function defined by g (x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest less than or equal to x.

Answer 1

Let g (x) = h (x) – q (x) 

where h (x) = x and q (x) = [x] 

h (x) = x, being a polynomial function continuous every where q (x) = [x]