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We are given two functions:  
- \( f(x) = x^3 + 4 \)  
- \( g(x) = x^2 - 9 \).

We are asked to find \( f - g \), which means we need to subtract \( g(x) \) from \( f(x) \).

### Step-by-step solution:

\[
f(x) - g(x) = (x^3 + 4) - (x^2 - 9)
\]

Now, distribute the negative sign:

\[
f(x) - g(x) = x^3 + 4 - x^2 + 9
\]

Simplify the expression:

\[
f(x) - g(x) = x^3 - x^2 + 13
\]

Thus, the rule for the function \( f - g \) is:

\[
f - g = x^3 - x^2 + 13
\]

Let me know if you have questions or need more details!

### Related questions:
1. How would you find \( f + g \) for the given functions?
2. What is the domain of the function \( f - g \)?
3. How would you find \( f(x) \cdot g(x) \) for these functions?
4. Can you differentiate \( f - g \) with respect to \( x \)?
5. What are the roots of the function \( f - g = 0 \)?

### Tip:
When subtracting functions, always distribute the negative sign carefully to avoid errors in combining terms!

Let f(x) = x^3 + 4 and g(x) = x^2 - 9. Find the rule for the function f - g.

Learn how to subtract two functions f(x) = x^3 + 4 and g(x) = x^2 - 9. Step-by-step guide to find the rule for the function f - g. Suitable for students in Grades 9-10.

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