If $\cos ^{-1} x = y$,then . . . . . . .

The domain of the function $f(x) = \sqrt{2 - \sec^{-1}x}$ is:

The function $f(x) = \sin^{-1}(\sqrt{x})$ is defined in the interval:

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

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