To find $f \circ g$, we need to evaluate $f(g(x))$, which means we substitute $g(x)$ into $f(x)$.

Given the functions:

• $f(x) = 3x - 9$
• $g(x) = x^3 + 1$

Step 1: Substitute $g(x)$ into $f(x)$

$f(g(x)) = 3(g(x)) - 9$ Since $g(x) = x^3 + 1$, substitute this into $f(g(x))$: $f(g(x)) = 3(x^3 + 1) - 9$

Step 2: Simplify the expression

$f(g(x)) = 3x^3 + 3 - 9$ $f(g(x)) = 3x^3 - 6$

Thus, $f \circ g = 3x^3 - 6$.

Would you like to proceed with $g \circ f$? Let me know if you want more details or have any questions.

Here are 5 questions related to the problem:

1. What is the domain of the function $f \circ g$?
2. How does the composition of functions affect their range?
3. Can the order of composition $f \circ g$ change the result compared to $g \circ f$?
4. What happens if $g(x)$ is a non-polynomial function?
5. How do we interpret function composition graphically?

Tip: Always pay attention to the domain of both functions when performing compositions to avoid undefined values!