Determine whether the following functions are even or odd or neither even nor odd :

$f\left(x\right)=\sin x+\cos x$  

Determine whether the following functions are even or odd or neither even nor odd :

vi) $f\left(x\right)=\left\{\begin{array}{cc}\left|\ln e^x\right|& ; x\le -1\\ [2+x]+[2-x]& ;-1<x<1\\ e^{\ln x}& ; x\ge 1\end{array}\right.$, where $\left[.\right]$ is the greatest integer function.

Examine whether the following functions are even or odd or neither even nor odd, .

 $f\left(x\right)=\frac{{\left(1+2^x\right)}^7}{2^x}$       

Examine whether the following functions are even or odd or neither even nor odd, where [ ] denotes the greatest integer function.

$f\left(x\right)=\frac{\sec x+x^2-9}{x\sin x}$            

Examine whether the following functions are even or odd or neither even nor odd, where [ ] denotes greatest integer function.$f\left(x\right)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$              

Examine whether the following functions are even or odd or neither even nor odd, where $\left[.\right]$ denotes the greatest integer function.

(iv) $f\left(x\right)=\left\{\begin{array}{cc}x\left|x\right|,& x\le -1\\ [1+x]+[1-x],& -1<x<1\\ -x\left|x\right|,& x\ge 1\end{array}\right.$

Which of the following functions are not periodic (where $[.]$ denotes the greatest integer function):

(i) $f\left(x\right)=\sin \sqrt{x}$                                                      (ii) $f\left(x\right)=x+\sin x$
(iii) $f\left(x\right)=\left[\sin 3x\right]+\left|\cos 6x\right|$

Find the fundamental period of the following functions:

(i) $f\left(x\right)=2+3\cos (x-2)$     

Find the fundamental period of $f\left(x\right)=\sin 3x+{\cos }^{2}x+\left|\tan x\right|$.