Answer
Domain: $ -\frac{2}{3}\leq x\leq0$
Range: $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$
Work Step by Step
Since the $\sin^{-1}$ function can only accept values between $-1$ and $1$,
$-1\leq 3x+1\leq1$
$-2\leq 3x\leq0$
$\therefore -\frac{2}{3}\leq x\leq0$
$g(x)$ like the standard $f(x)=\sin^{-1}(x)$ will produce values between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ as its inputs are the same (all real values between $-1$ and $1$). So its range is $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$
