Domain of a Function

Q. Inverse of All trigonometric functions exist over their respective domains.

1. False
2. True

Q. The range of ${\sin }^{-1}\left(2^x\right)$ is

1. $\left(\frac{-\pi }{2},\frac{\pi }{2}\right]$
2. $(0,\frac{\pi }{2}]$
3. $(0,\pi )$
4. $\left(0,\pi \right]$