If the functions are combined so that *h*(*x*) = *f*(*x*) – *g*(*x*), then the domain of the function *h*(*x*) is *x ≥*

To find the domain of the function \( h(x) = f(x) - g(x) \), we need to consider the domains of both functions \( f(x) \) and \( g(x) \). The domain of \( h(x) \) will be the intersection of the domains of \( f(x) \) and \( g(x) \). 

Let's define it step-by-step:

1. **Determine the domain of \( f(x) \)**: Identify where \( f(x) \) is defined (e.g., values of \( x \) where the function does not involve division by zero, square roots of negative numbers, etc.).

2. **Determine the domain of \( g(x) \)**: Similarly, identify where \( g(x) \) is defined.

3. **Combine the domains**: The domain of \( h(x) \) is the intersection of the domains of \( f(x) \) and \( g(x) \). This means \( h(x) \) is defined only for values of \( x \) that are valid for both \( f(x) \) and \( g(x) \).

Therefore, without specific details about \( f(x) \) and \( g(x) \), the domain of \( h(x) \) would be determined by the constraints present in both functions.

### Example Scenario:
- If \( f(x) \) is defined for \( x \ge 0 \) and \( g(x) \) is defined for \( x > -2 \), then the combined domain \( h(x) = f(x) - g(x) \) would be \( x \ge 0 \), since it is the more restrictive condition.

Would you like to see more specific examples or details about finding domains with particular functions?

### Follow-up Questions:
1. What are the specific functions \( f(x) \) and \( g(x) \) you are working with?
2. Do you need help finding the domain of a particular type of function, such as a rational or square root function?
3. Are there any known restrictions or conditions for \( f(x) \) and \( g(x) \)?
4. Would you like to see how different combinations of domains affect the final domain?
5. How does the domain affect the graph of the function \( h(x) \)?

**Tip**: Always pay close attention to restrictions like division by zero and square roots of negative numbers when determining the domain of combined functions.

Learn how to determine the domain of the function h(x) = f(x) - g(x) by analyzing the domains of f(x) and g(x). This problem involves understanding function domains and their intersections, crucial for advanced high school mathematics.

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