https://file.aiquickdraw.com/mathbot/file/17280426328642amo39sm.jpg

The functions given in the image are:

\[
f(x) = \frac{x + 4}{x}, \quad g(x) = \frac{4}{x - 1}
\]

Would you like to compute the composition of these functions (like \( f(g(x)) \) or \( g(f(x)) \)) or some other operation? Let me know what you'd like to explore further!

Here are a few related questions you might consider:

1. What is the domain of \( f(x) \) and \( g(x) \)?
2. Can we simplify the expression for \( f(x) \)?
3. What is \( f(g(x)) \) and how can we compute it?
4. What happens if we solve \( f(x) = g(x) \)?
5. How do the graphs of \( f(x) \) and \( g(x) \) behave?

**Tip:** When working with rational functions, always remember to check for any restrictions on the domain based on where the denominators could become zero!

Learn how to work with the rational functions f(x) = (x + 4)/x and g(x) = 4/(x - 1). This includes exploring domains, simplifying expressions, and composing functions. Suitable for Grades 9-11 students studying algebra.

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