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We are given the functions \( f(x) = 3x + 6 \) and \( g(x) = -7 \), and asked to calculate the following:

### Part (a): \( f(g(8)) \)
- First, note that \( g(x) = -7 \) for all \( x \), so \( g(8) = -7 \).
- Now, substitute this value into \( f(x) \):
  \[
  f(g(8)) = f(-7) = 3(-7) + 6 = -21 + 6 = -15
  \]
  So, \( f(g(8)) = -15 \), which is correctly calculated in the given solution.

### Part (d): \( g(f(-1)) \)
- First, calculate \( f(-1) \):
  \[
  f(-1) = 3(-1) + 6 = -3 + 6 = 3
  \]
- Now, substitute this value into \( g(x) \). Since \( g(x) = -7 \) for all \( x \), we have:
  \[
  g(f(-1)) = g(3) = -7
  \]
  So, \( g(f(-1)) = -7 \).

If you'd like more details or have any questions, let me know!

Here are 5 related questions:
1. What is \( f(g(2)) \)?
2. What is \( g(f(0)) \)?
3. What is \( f(f(-2)) \)?
4. If \( g(x) = 2x - 5 \), what would \( g(f(4)) \) be?
5. Can \( g(x) \) ever be anything other than -7 for the given function?

**Tip:** When dealing with function compositions, always evaluate the inner function first, then use the result in the outer function.

Given that f(x) = 3x + 6 and g(x) = -7, calculate the following: (a) f(g(8)), (d) g(f(-1))

Learn how to solve function composition problems like f(g(8)) and g(f(-1)) using the functions f(x) = 3x + 6 and g(x) = -7. This example demonstrates evaluating inner functions first and then applying the outer function, suitable for students in Grades 8-10.

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