The domain of the function defined by $f(x) = \cos^{-1} \sqrt{x-1}$ is

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

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

The domain of the function $f(x) = \sin^{-1}[\log_2(x/2)]$ is

Domain of the function $f(x) = \sin^{-1}\left(\frac{2-|x|}{4}\right) + \cos^{-1}\left(\frac{2-|x|}{4}\right) + \tan^{-1}\left(\frac{2-|x|}{4}\right)$ is

The range of $\sec ^{-1} x$ is