(a) Find the domain of y= sin^-1( x^2-4).

Domain of $\displaystyle \sin ^{-1} \mathrm{x}$ is $\displaystyle -1 \leq \mathrm{x} \leq 1$

$$\therefore-$\displaystyle 1$ \leq \mathrm{x}^{$\displaystyle 2$}-$\displaystyle 4$ \leq $\displaystyle 1$

$$or $\displaystyle \mathrm{x}^{2} \geq 3, \mathrm{x}^{2} \leq 5$

∴ Domain is $\displaystyle [-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]$

$\displaystyle \cos ^{-1}\left[\cos \left(-\frac{7 \pi}{3}\right)\right]=\cos ^{-1}\left[\cos \left(\frac{7 \pi}{3}\right)\right]$

$$=\cos ^{-$\displaystyle 1$}\left[\cos \left(2 \pi+\frac{\pi}{3}\right)\right]