Question

The function f(x) = [x]^n - [x^n], for n > or = 2 ( where [a] denotes the greatest integer less than or equal to 'a'), is discontinuous at all points of:

1. all integers
2. all integers except 0 and 1
3. all integers except 0
4. all integers except 1

answer: (4)

{ Please give me a descriptive answer rather than just solution and thanks in advance}