Find the domain of function: `f(x)=sin^(-1)sqrt(x^2-1)`

Explanation

To find the domain of the function \( f(x) = \sin^{-1}(\sqrt{x^2 - 1}) \), we need to determine the values of \( x \) for which the expression inside the inverse sine function is valid.

### Step-by-Step Solution:

1. **Understand the Range of the Inverse Sine Function**:
The function \( \sin^{-1}(y) \) is defined for \( y \) in the range \([-1, 1]\). Therefore, we need to ensure that:
\[
-1 \leq \sqrt{x^2 - 1} \leq 1
...