Find the domain and range of the following function.

$y={\cot }^{-1}\left(2x-x^2\right)$

Find the domain and range of the following function.

$f\left(x\right)={\sec }^{-1}\left({\log }_3\tan x+{\log }_{\tan x}3\right)$

Find the domain and range of the following functions.

$f\left(x\right)=2^{{\cos }^{-1}\left(\sin \left(x+\frac{\pi }{3}\right)\right)}+\left[\frac{\sqrt{1-2\cos x}}{2}\right]$

where, $\left[·\right]$ is the greatest integer function.

Find the domain and range of the following functions.

$f\left(x\right)={\tan }^{-1}\left({\log }_{\frac{4}{5}}\left(5x^2-8x+4\right)\right)$

Draw the graph of the following function:

$f\left(x\right)={\sin }^{-1}\left(x+2\right)$

Draw the graph of the following function:

$g\left(x\right)=\left[{\cos }^{-1}x\right]$, where $\left[·\right]$ denotes greatest integer function.

Draw the graph of the following function:

$h\left(x\right)=-\left|{\tan }^{-1}\left(3x\right)\right|$

Express $f\left(x\right)={\cos }^{-1}x+{\cos }^{-1}\left(\frac{x}{2}+\frac{1}{2}\sqrt{3-3x^2}\right)$ in simplest form and hence find the values of

$f\left(\frac{2}{3}\right)$

Express $f\left(x\right)=\mathrm{arc} \cos x+\mathrm{arc} \cos \left(\frac{x}{2}+\frac{1}{2}\sqrt{3-3x^2}\right)$ in simplest form and hence find the value of $f\left(\frac{1}{3}\right)$.