Odd Function

Q. If $f\left(x\right)=\frac{\cos x}{\left[\frac{x}{\pi }\right]+\frac{1}{2}},$ where $x$ is not an integral multiple of $\pi$ and $[.]$ denotes the greatest integer function, then

1. $f\left(x\right)$ is an even function
2. $f\left(x\right)$ is an odd function
3. $f\left(x\right)$ is neither even nor odd
4. None of these