We are tasked with evaluating $f(g(-3))$.

Given functions:

• $f(x) = x^2 - 20$
• $g(x) = 4 + 3x$

Let's break it down:

1. First, find $g(-3)$: $g(-3) = 4 + 3(-3) = 4 - 9 = -5$

2. Now, plug $g(-3) = -5$ into $f(x)$: $f(-5) = (-5)^2 - 20 = 25 - 20 = 5$

Thus, $f(g(-3)) = 5$.

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Would you like more details or explanations on this solution? Here are some related questions to explore:

1. How would the result change if the function $g(x)$ were different?
2. How do we handle the composition of two functions in general?
3. What would happen if we substituted another value into $g(x)$?
4. How do you evaluate compositions when functions involve more complex expressions?
5. What’s the significance of function composition in real-life scenarios?

Tip: When working with function compositions, always remember to first evaluate the inner function and then substitute its result into the outer function!