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

If the domain of the function $f(x) = \sin^{-1}\left(\frac{2}{x^2-2x-2}\right)$ is $(-\infty, \alpha] \cup [\beta, \gamma] \cup [\delta, \infty)$,then $\alpha + \beta + \gamma + \delta$ is equal to

The domain of the derivative of the function $f(x) = \operatorname{Cos}^{-1}(2x - 5) - \operatorname{Sin}^{-1}(x - 2)$ is

The domain of the function $f(x) = \sin^{-1}\left(\frac{|x|+5}{x^2+1}\right)$ is $(-\infty, -a] \cup [a, \infty)$. Then $a$ is equal to

Let $[x]$ denote the greatest integer less than or equal to $x$. Then the domain of $f(x) = \sec^{-1}(2[x] + 1)$ is:

The domain of $\sin^{-1}x$ is