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

Find the fundamental period of the following functions : $f\left(x\right)=\sin \frac{\mathrm{\pi }x}{4}+\sin \frac{\mathrm{\pi }x}{3}$               

Find the fundamental period of the following functions: $f\left(x\right)=\cos \frac{3}{5}x-\sin \frac{2}{7}x$

Find the fundamental period of the following functions:

$\begin{array}{ll}\text{ (v) }& f\left(x\right)=\frac{1}{1-\cos x}\end{array}$                      

Find the fundamental period of the following function  $f\left(x\right)=\frac{\sin 12x}{1+{\cos }^{2}6x}\begin{array}{}\end{array}$                                

Find the fundamental period of the following function $\mathrm{f}\left(\mathrm{x}\right)={\sec }^{3}x+{cosec}^{3}x$

Let $f: D\to R,$ where $D$ is the domain of $f$. Find the inverse of $f$, if it exists, $f\left(x\right)=1-2^{-x}$.