Question

If a, b ∈ R, then the period of f(x) = x − [x + a] − b, where [·] denotes the greatest integer function, is 

(A)  1

(B)  |a − b| 

(C)  |a + b|

(D)  None of these

Answer 1

Correct option (A) 1

Explanation :

f(x) = x + a − [x + a] − b – a ⇒ f(x) = {x + a} − b – a Hence, f(x) is periodic with 1.