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The problem asks to determine the domain of the function \( q(x) = \frac{g(x)}{f(x)} \).

To find the domain of \( q(x) \), we need to consider the following:

1. **The domain of \( g(x) \)**: \( g(x) \) must be defined for a particular \( x \).
2. **The domain of \( f(x) \)**: \( f(x) \) must also be defined for a particular \( x \), but since \( f(x) \) is in the denominator, it cannot be equal to zero. 

Thus, the domain of \( q(x) \) will be all the values of \( x \) such that:
- \( g(x) \) is defined.
- \( f(x) \) is defined and \( f(x) \neq 0 \).

In summary, the domain of \( q(x) \) is:
\[
\text{Domain of } q(x) = \{x \in \mathbb{R} \mid g(x) \text{ is defined and } f(x) \neq 0 \}.
\]

Would you like to go into more detail or discuss specific cases of \( f(x) \) and \( g(x) \)?

Here are 5 related questions:
1. What happens to the domain of a function when both \( g(x) \) and \( f(x) \) are polynomials?
2. How do you handle cases where \( g(x) \) is undefined at certain points?
3. Can the domain be affected by additional restrictions on \( x \)?
4. What would happen if \( g(x) \) is a trigonometric function?
5. How do you graph the domain restrictions for rational functions?

**Tip:** Always check for values that make the denominator zero when dealing with rational functions to avoid undefined points in the domain.

Jika q(x) = g(x) / f(x), tentukan domain q(x).

Find the domain of the rational function q(x) = g(x) / f(x). The domain includes all values of x such that g(x) is defined and f(x) is non-zero. This solution covers key concepts in algebra and functions for students in Grades 10-12.

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