Question

The function f(x) = x – [x], where [.] denotes the greatest integer function is

A. Continuous everywhere

B. Continuous at integer points only

C. Continuous at non-integer points only

D. Differentiable everywhere

Answer 1

Correct answer is C.

Given function f(x) = x – [x]

For any integer n,

Hence, f(x) is not continuous at integer points.

∴ Given function is continuous on non integer points only.