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

Domain of the function $f(x) = \frac{1}{\sqrt{\ln(\cot^{-1}x)}}$ is

The domain of $f(x) = \cos^{-1}[x]$ is,where $[x]$ denotes the greatest integer function.

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 $.......$.

Domain of definition of the real valued function $f(x) = \sqrt{\sin^{-1}(2x) + \frac{\pi}{6}}$ is

Range of the function $f(x) = \cot^{-1} \left( \log_{4/5} (5x^2 - 8x + 4) \right)$ is: