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To evaluate \((gh)(-3)\), we need to multiply the functions \(g(x)\) and \(h(x)\), and then substitute \(x = -3\).

Given:
\[
g(x) = \frac{2}{x + 2}
\]
\[
h(x) = -3x + 2
\]

### Step 1: Calculate \(g(-3)\)
Substitute \(x = -3\) into \(g(x)\):
\[
g(-3) = \frac{2}{-3 + 2} = \frac{2}{-1} = -2
\]

### Step 2: Calculate \(h(-3)\)
Substitute \(x = -3\) into \(h(x)\):
\[
h(-3) = -3(-3) + 2 = 9 + 2 = 11
\]

### Step 3: Multiply \(g(-3)\) and \(h(-3)\)
\[
(gh)(-3) = g(-3) \times h(-3) = (-2) \times 11 = -22
\]

Thus, the value of \((gh)(-3)\) is:
\[
(gh)(-3) = -22
\]

Would you like further details or explanations? Here are some related questions:

1. How do you interpret the product of two functions in general?
2. Can the function \(g(x)\) have any undefined points?
3. How would you evaluate \( (fg)(x) \) for the same functions?
4. Can you graph the functions \(g(x)\) and \(h(x)\)?
5. What happens to the product of \(g(x)\) and \(h(x)\) for other values of \(x\)?

**Tip:** When multiplying functions, always compute each function's value first before multiplying the results.

Evaluate (gh)(-3) for the functions g(x) = 2/(x + 2) and h(x) = -3x + 2.

Learn how to evaluate the product of two functions g(x) = 2/(x + 2) and h(x) = -3x + 2 at x = -3. This problem covers the core concepts of function multiplication and substitution. Suitable for high school students in Grades 9-12.

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