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To solve \((fg)(-8)\), where \( f(x) = x + 3 \) and \( g(x) = x^2 - 2 \), we need to evaluate the product of the functions \( f(x) \) and \( g(x) \) at \( x = -8 \).

### Step-by-step solution:

1. **Find \( f(-8) \):**
   \[
   f(x) = x + 3
   \]
   Substituting \( x = -8 \):
   \[
   f(-8) = -8 + 3 = -5
   \]

2. **Find \( g(-8) \):**
   \[
   g(x) = x^2 - 2
   \]
   Substituting \( x = -8 \):
   \[
   g(-8) = (-8)^2 - 2 = 64 - 2 = 62
   \]

3. **Multiply the results:**
   Now, \((fg)(-8)\) is the product of \( f(-8) \) and \( g(-8) \):
   \[
   (fg)(-8) = f(-8) \times g(-8) = -5 \times 62 = -310
   \]

So, \((fg)(-8) = -310\).

Would you like any further details or clarifications? 

Here are 5 related questions:
1. How do you find the sum of two functions at a particular value?
2. How would the result change if the function \( g(x) \) had a different power (e.g., \( g(x) = x^3 - 2 \))?
3. What is the domain of the function product \( f(x) \cdot g(x) \)?
4. How can we graph the function \( f(x) \cdot g(x) \) for all \( x \)?
5. Can this process be extended to more complicated functions, such as trigonometric functions?

**Tip**: When multiplying functions, always evaluate each function individually first before performing any operations on the results!

Evaluate the function for f(x) = x + 3 and g(x) = x^2 - 2. Find (fg)(-8).

Learn how to evaluate the product of two functions, f(x) = x + 3 and g(x) = x^2 - 2, at a specific value x = -8. Follow a step-by-step solution suitable for students in Grades 9-12.

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