Find the domain of `f(x)=sin^(-1){(log)_9((x^2)/4)}`

Explanation

To find the domain of the function \( f(x) = \sin^{-1}\left(\log_9\left(\frac{x^2}{4}\right)\right) \), we need to ensure that the argument of the sine inverse function is within the range \([-1, 1]\). This means we need to solve the inequality:

\[ -1 \leq \log_9\left(\frac{x^2}{4}\right) \leq 1 \]

### Step 1: Solve the left part of the inequality
Starting with the left part of the inequality:
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