Find the domain of the function \(f(x) = \frac{1}{\sqrt{x^2 - 9}}\)

Step 1 ：To find the domain of the function, we first look at the denominator \(\sqrt{x^2 - 9}\). We know that the value under the square root must be greater than or equal to 0. So, \(x^2 - 9 \geq 0\)

Step 2 ：Solving the inequality gives us two possibilities: \[x \leq -3\] or \[x \geq 3\]

Step 3 ：However, because we're dealing with a rational function, we need to ensure that the denominator is not equal to 0. So the domain of the function is \(x < -3\) or \(x > 3\)