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

Considering only the principal values of the inverse trigonometric functions,the domain of the function $f(x) = \cos^{-1}\left(\frac{x^{2}-4x+2}{x^{2}+3}\right)$ is:

Range of $f(x) = \sin^{-1} (\sqrt{x^2 + x + 1})$ is -

The domain of $f(x) = \frac{1}{{\sqrt {{{\log }_{\frac{\pi }{4}}}({{\sin }^{ - 1}}x) - 1} }}$ is:

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