The domain of $\sin^{-1}[\log_3(\frac{x}{3})]$ is:

[1, 9] [-1, 9] [-9, 1] [-9, -1]

[1, 9]

$f(x)=\sin^{-1}(\log_3(\frac{x}{3}))$ exists If $-1≤\log_3(\frac{x}{3})≤1⇔3^{-1}≤\frac{x}{3}≤3^1$ ⇔ 1 ≤ x ≤ 9 or x ∈ [1, 9]