Question

The function f(x) = [x]² - [x²] (where [x] is the greatest integer less than or equal to x), is discontinuous at

(a) all integers

(b) all integers except 0 and 1

(c) all integers except 0

(d) all integers except 1

Answer 1

Correct option (b) all integers except 0 and 1

Explanation :

All integers ore critical point for greatest integer function.

This shows that f(x) is continuous at x = 1

Therefore, f(x) is discontinuous in 

on many other points .