https://file.aiquickdraw.com/mathbot/file/1726882198916v4gpgvdn.jpg

Let's analyze the given functions and the problem.

### Given Functions:
1. \( f(x) = -3x \)
2. \( g(x) = |x - 4| \)
3. \( h(x) = \frac{1}{x + 7} \)

### Task:
Evaluate the function \( (f - g)(x) \) for \( x = -5 \).

### Calculation:
1. **Find \( f(-5) \):**
   \[
   f(-5) = -3(-5) = 15
   \]

2. **Find \( g(-5) \):**
   \[
   g(-5) = |-5 - 4| = |-9| = 9
   \]

3. **Find \( (f - g)(-5) \):**
   \[
   (f - g)(-5) = f(-5) - g(-5) = 15 - 9 = 6
   \]

Therefore, \( (f - g)(-5) = 6 \).

The error in the given image is because the calculated value of \( (f - g)(-5) \) is shown as \(-7\), which is incorrect. The correct answer should be 6.

Would you like more details or have any questions?

### Related Questions:
1. What is the value of \( (f \cdot g)(x) \) for \( x = -5 \)?
2. How would you find \( (f + g)(x) \) for any \( x \)?
3. What is the domain of the function \( h(x) \)?
4. How does the graph of \( g(x) = |x - 4| \) look like?
5. Can \( h(x) \) be evaluated for \( x = -7 \)?

**Tip:** Always double-check calculations and the interpretation of functions, especially when absolute values and subtractions are involved.

Evaluate the function (f - g)(x) for x = -5, given f(x) = -3x, g(x) = |x - 4|, and h(x) = 1/(x + 7).

This problem involves evaluating the difference of two functions, f(x) = -3x and g(x) = |x - 4|, for x = -5. The step-by-step solution covers linear and absolute value functions and is suitable for high school students in Grades 9-11.

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