The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$ is

The range of the real valued function $f(x) = \operatorname{Cos}^{-1}\left(\frac{3}{\sqrt{9x^2 - 12x + 22}}\right)$ is

The domain of $f(x) = \sin^{-1}\left[\log_{2}\left(\frac{x}{2}\right)\right]$ is

The domain of $f(x) = \cos^{-1}[x]$ is,where $[x]$ denotes the greatest integer function.

The domain of the function $f(x) = \frac{\sin^{-1}(x - 3)}{\sqrt{9 - x^2}}$ is

If the domain of the function $f(x) = \cos^{-1}(\frac{2x-5}{11-3x}) + \sin^{-1}(2x^2-3x+1)$ is the interval $[\alpha, \beta]$, then $\alpha + 2\beta$ is equal to: