Domain of $\sin^{-1}$ is . . . . . . .

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x) = \sin^{-1} \left( \frac{x+[x]}{3} \right)$ is $[\alpha, \beta)$, then $\alpha^2 + \beta^2$ is equal to:

Domain of $\cos ^{-1}\left[\log _5\left(x^2+7 x+15\right)\right]$ is

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

Domain of function $f(x) = \sin^{-1}(5x)$ is

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