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Let's solve the given problem step by step.

We are given two functions:
1. \( f(x) = x^2 + x - 6 \)
2. \( g(x) = \frac{x - 2}{x + 3} \)

We are tasked with finding \( f(g(2)) \).

### Step 1: Compute \( g(2) \)
Using the definition of \( g(x) \), substitute \( x = 2 \):

\[
g(2) = \frac{2 - 2}{2 + 3} = \frac{0}{5} = 0
\]

So, \( g(2) = 0 \).

### Step 2: Compute \( f(g(2)) = f(0) \)
Now that we know \( g(2) = 0 \), we substitute \( x = 0 \) into the function \( f(x) \):

\[
f(0) = 0^2 + 0 - 6 = -6
\]

Therefore, \( f(g(2)) = -6 \).

### Final Answer: 
The value of \( f(g(2)) \) is \( -6 \), so the correct option is \( -6 \).

Would you like more details on any part of this solution?

Here are 5 related questions to expand your understanding:
1. What happens if \( g(x) \) has a denominator that can cause division by zero?
2. Can we generalize this process for different functions \( f(x) \) and \( g(x) \)?
3. What is the domain of the composite function \( f(g(x)) \)?
4. How do we differentiate \( f(g(x)) \) if both functions are differentiable?
5. What is the importance of the order in which we apply functions in composition?

**Tip:** When working with function compositions, always check the domain of each function to avoid undefined values.

If f(x) = x^2 + x - 6 and g(x) = (x - 2) / (x + 3), then f(g(2))?

Learn how to evaluate the composite function f(g(2)) where f(x) = x^2 + x - 6 and g(x) = (x - 2) / (x + 3). This step-by-step solution includes key algebraic concepts such as function composition and solving quadratic and rational functions. Suitable for students in Grades 9-11.

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