The period of function `2^({x}) +sin pi x+3^({x//2})+cos pi x` (where {x} denotes the fractional part of x) is

Options

A. 2
B. 1
C. 3
D. None of these

Answer

A

Explanation

The period of `sin pi x and cos pi x ` is 2 and 1, respectively.
The period of `2^({x})` is 1.
The period of `3({x//2})` is 2.
Hence, the period of `f(x)` is LCM of 1 and 2, i.e., 2.