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The uploaded image contains a math task related to the characteristics of functions. Here's a breakdown of the task:

### 1. Given \( f(g(x)) = \sqrt[3]{x^3 - 24x^2 + 24x - 8} \), state two different possible sets of functions for \( f(x) \) and \( g(x) \).

This part asks you to find two possible pairs of functions \( f(x) \) and \( g(x) \) such that their composition \( f(g(x)) \) gives the given function.

### 2. Fill in each "x" with the last digit of your student number.

Given: 
\[
f(x) = x^x, \quad g(x) = -\sin(x), \quad h(x) = \log(x - 1), \quad m(x) = x^3
\]

- **Part a**: Simplify \( g(x) - m(x) \) and find the domain.
- **Part b**: Simplify \( f(h(x)) \) and find the domain.
- **Part c**: Simplify \( h(g(x)) \) and find the domain.

#### Instructions:
- Simplify the expressions for each part.
- Identify the domain of the simplified functions.

Would you like to proceed with solving one of these parts, or would you prefer more detailed assistance with the entire task? Let me know how you'd like to proceed.

Here are five related questions you might consider:
1. How do you determine the domain of a composite function?
2. What are some methods to simplify composite functions?
3. How does the behavior of \( \sin(x) \) affect the domain when it's part of a composite function?
4. What rules apply when simplifying logarithmic expressions like \( \log(x - 1) \)?
5. How does the cubic function \( x^3 \) impact the overall function when subtracted from another function?

**Tip**: Always ensure that the domain of the inner function is considered when finding the domain of the composite function.

Explore a breakdown of a math problem involving function composition and domain. Learn how to simplify composite functions and determine their domains. Suitable for undergraduate students studying advanced calculus.

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