To solve for the composite function $(g \circ f)(x)$, we substitute $f(x)$ into $g(x)$:

Given Functions:

• $f(x) = \frac{x - 3}{9}$
• $g(x) = 9x + 3$

Step 1: Find $(g \circ f)(x) = g(f(x))$

Substitute $f(x) = \frac{x - 3}{9}$ into $g(x) = 9x + 3$: $g(f(x)) = 9\left(\frac{x - 3}{9}\right) + 3$

Step 2: Simplify

Distribute $9$ into $\frac{x - 3}{9}$: $g(f(x)) = (x - 3) + 3$

Simplify further: $g(f(x)) = x$

Final Answer:

The composite function $(g \circ f)(x) = x$.

Correct Option:

The correct choice is "x".

Would you like additional clarification or step-by-step breakdowns of related concepts? Here are some questions for exploration:

1. What is the significance of composite functions in mathematics?
2. How does substituting functions work in different contexts?
3. Can you show how to find $f(g(x))$ for the same functions?
4. Why does this composition simplify to $x$ in this case?
5. How does the order of composition affect the outcome?

Tip: Always ensure to simplify step-by-step to avoid errors when working with composite functions!