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

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

Let $f$ be a real valued function defined by $f(x) = \sin^{-1} \left( \frac{1 - |x|}{3} \right) + \cos^{-1} \left( \frac{|x| - 3}{5} \right)$. Then the domain of $f(x)$ is given by:

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

If the domain of the function $f(x) = \sec^{-1}\left(\frac{2x}{5x+3}\right)$ is $[\alpha, \beta) \cup (\gamma, \delta]$,then $|3\alpha + 10(\beta + \gamma) + 21\delta|$ is equal to $.......$.

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