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Let's go through the problem you posted.

We are given two functions:

- \( f(x) = x - 5 \)
- \( g(x) = (x - 4)(x + 4) \)

### (a) Find \( \left( \frac{f}{g} \right)(-2) \).

This means we need to evaluate \( \frac{f(x)}{g(x)} \) at \( x = -2 \).

1. First, find \( f(-2) \):
   \[
   f(-2) = -2 - 5 = -7
   \]

2. Now, find \( g(-2) \):
   \[
   g(-2) = (-2 - 4)(-2 + 4) = (-6)(2) = -12
   \]

3. Now, calculate \( \left( \frac{f}{g} \right)(-2) \):
   \[
   \left( \frac{f}{g} \right)(-2) = \frac{-7}{-12} = \frac{7}{12}
   \]

### (b) Find all values that are **NOT** in the domain of \( \frac{f}{g} \).

The domain of \( \frac{f}{g} \) consists of all values of \( x \) for which \( g(x) \neq 0 \). So, we need to find when \( g(x) = 0 \).

\( g(x) = (x - 4)(x + 4) \) equals zero when \( x = 4 \) or \( x = -4 \). Thus, the values that are **not** in the domain of \( \frac{f}{g} \) are \( x = 4 \) and \( x = -4 \).

---

### Final Answers:
- (a) \( \left( \frac{f}{g} \right)(-2) = \frac{7}{12} \)
- (b) Values **not** in the domain of \( \frac{f}{g} \): \( 4, -4 \)

Would you like further clarification or details on any part of this? Here are some related questions you might find useful:

1. How do you determine the domain of a quotient of functions?
2. What happens if you try to divide by zero in functions?
3. How do you factor quadratics like \( g(x) = (x - 4)(x + 4) \)?
4. What are the key differences between the domain of \( f(x) \) and \( g(x) \)?
5. How can you visually represent the domain and range of a function?

**Tip:** Always remember to check for values that make the denominator zero when dealing with rational functions!

Suppose that the functions f and g are defined as follows: f(x) = x - 5 and g(x) = (x - 4)(x + 4). (a) Find (f/g)(-2). (b) Find all values that are NOT in the domain of f/g.

Learn how to find the quotient of two functions f(x) = x - 5 and g(x) = (x - 4)(x + 4) at a specific value and identify the domain restrictions caused by division by zero. This problem is perfect for students in Grades 9-11.

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