The domain of the function $f(x) = \sin^{-1}\left(\log_2\left(\frac{x^2}{2}\right)\right)$ is

The domain of the function $f(x) = \sin^{-1}\left(\frac{x^{2}-3x+2}{x^{2}+2x+7}\right)$ is:

The number of real roots of the equation $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{4}$ is:

The domain of ${\sin ^{ - 1}}({\log _3}x)$ is

If the domain of the function $f(x) = \sin^{-1}\left(\frac{5-x}{3+2x}\right) + \frac{1}{\log_e(10-x)}$ is $(-\infty, \alpha] \cup [\beta, \gamma) - \{\delta\}$, then $6(\alpha + \beta + \gamma + \delta)$ is equal to

If $y = \operatorname{cosec}^{-1}(x)$ and $\frac{dy}{dx} = \frac{-1}{|x| \sqrt{x^2-1}}$,then