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!