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To solve the problem, we need to evaluate \( f(-2 - g(3)) \).

First, let's find \( g(3) \):
\[ g(x) = x^2 - 3 \]
\[ g(3) = 3^2 - 3 = 9 - 3 = 6 \]

Next, we need to calculate \( -2 - g(3) \):
\[ -2 - g(3) = -2 - 6 = -8 \]

Now, we will find \( f(-8) \):
\[ f(x) = \frac{3}{4}x + 10 \]
\[ f(-8) = \frac{3}{4}(-8) + 10 = \frac{3 \cdot (-8)}{4} + 10 = \frac{-24}{4} + 10 = -6 + 10 = 4 \]

So, the value of \( f(-2 - g(3)) \) is \( 4 \).

Would you like more details or have any questions?

Here are 8 related questions to further your understanding:
1. How do you find the value of \( g(x) \) for any \( x \)?
2. How does the function \( f(x) = \frac{3}{4}x + 10 \) change as \( x \) increases?
3. What is the effect of substituting a negative value into \( f(x) \)?
4. How would you solve \( f(x) = 0 \) for \( x \)?
5. What is the range of the function \( g(x) = x^2 - 3 \)?
6. How do you determine the domain of the function \( f(x) \)?
7. Can you find \( f(g(x)) \) for any \( x \)?
8. How would you graph the function \( f(x) = \frac{3}{4}x + 10 \)?

**Tip:** When evaluating composite functions, always start from the innermost function and work outward step by step.

Learn how to evaluate composite functions and solve for f(-2 - g(3)) with step-by-step explanations. This problem covers function evaluation, composite functions, and quadratic function formulas. Suitable for students in Grades 9-12.

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