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.