The domain of $\sin^{-1}[\log_3(\frac{x}{3})]$ is:
Answer & explanation
Correct answer: option 1
$f(x)=\sin^{-1}(\log_3(\frac{x}{3}))$ exists
If $-1≤\log_3(\frac{x}{3})≤1⇔3^{-1}≤\frac{x}{3}≤3^1$
⇔ 1 ≤ x ≤ 9 or x ∈ [1, 9]
The domain of $\sin^{-1}[\log_3(\frac{x}{3})]$ is:
Correct answer: option 1
$f(x)=\sin^{-1}(\log_3(\frac{x}{3}))$ exists
If $-1≤\log_3(\frac{x}{3})≤1⇔3^{-1}≤\frac{x}{3}≤3^1$
⇔ 1 ≤ x ≤ 9 or x ∈ [1, 9]