The file contains an activity related to the composition of functions. Specifically, the task is to find $(f \circ g)(x)$ and $(g \circ f)(x)$ for given pairs of functions.

Here are the functions from the document:

1. $f(x) = 7x - 1$, $g(x) = x - 1$
2. $f(x) = x$, $g(x) = \frac{1}{2x + 1}$
3. $f(x) = 4x - 5$, $g(x) = \frac{x + 5}{4}$
4. $f(x) = \frac{9 + x}{x}$, $g(x) = \frac{9 - x}{4x}$
5. $f(x) = 2x$, $g(x) = \frac{x}{2}$

Would you like me to compute the compositions for these functions? If so, I can start with one and go step by step.

Here are five related questions to consider:

1. What is the domain of $f \circ g$ for these functions?
2. How does the composition of two functions affect their range?
3. What happens if one of the functions is not one-to-one or onto?
4. Can you find an inverse function for any of these compositions?
5. What is the difference between $f \circ g$ and $g \circ f$ in terms of their graphical interpretation?

Tip: When composing functions, always simplify the inner function first to avoid errors during substitution.