The period of the function f(x) = [5x + 7] + cosp x – 5x, where [·] denotes the greatest integer function, is

Question

The period of the function f(x) = [5x + 7] + cosπ x – 5x, where [·] denotes the greatest integer function, is

(A)  3

(B)  2π

(C)  2

(D)  None of these

Answer 1

Correct option  (C) 2

Explanation :

We have

f(x) = −{(5x + 7) – [5x + 7]} + cosp x + 7 = − {5x + 7} + cosp x + 7 

The period of (5x + 7) is 1/5 and the period of cospx is 2. Therefore, the period of f(x) is 2.