The given function is:

$f(x) = \frac{10}{\sqrt{x^2 - 9}}$

Domain of the Function:

To determine the domain of the function, we must consider the conditions under which the square root and the denominator are defined.

1. The expression under the square root, $x^2 - 9$, must be greater than 0 because the square root of a negative number is not real and division by 0 is undefined.

   $x^2 - 9 > 0$

   Solving this inequality:

   $x^2 > 9$

   Taking the square root of both sides:

   $|x| > 3 \quad \text{or} \quad x > 3 \quad \text{or} \quad x < -3$

   Therefore, the domain of $f(x)$ is:

   $(-\infty, -3) \cup (3, \infty)$

Would you like further details or clarifications? Here are 5 questions to expand on this:

1. What happens to the function as $x$ approaches 3 from the right or left?
2. How would the graph of this function look?
3. How does the function behave for large values of $x$?
4. What is the range of the function?
5. How would you find the derivative of this function?

Tip: Always remember that when dealing with square roots in a function's denominator, ensure the expression inside is positive to avoid undefined values.