$\sin ^{-1}(x-1)+\cos ^{-1}(x-3)+\tan ^{-1}\left(\frac{x}{2-x^2}\right)=\cos ^{-1} k+\pi$, then the value of ' $k$ ' is

The value of $\tan \left\{\cos ^{-1}\left(\frac{\sqrt{2}}{2}\right)-\frac{\pi}{2}\right\}$ is

The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is

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