The worksheet you uploaded contains a set of functions and asks to perform operations like addition, subtraction, multiplication, division, or composition on them to achieve a result that matches one of the solutions listed (from "a" to "p"). Here are the given functions:

1. $g(x) = \frac{x}{4}$
2. $h(x) = x + 2$
3. $p(x) = 3x$
4. $q(x) = x - 5$
5. $r(x) = 7x$
6. $s(x) = x + 5$
7. $t(x) = \frac{1}{x}$
8. $v(x) = 2x$

Potential Solution:

Let's start by trying to create a function that matches one of the listed solutions using some of the operations.

1. Addition:
   Let's try adding $g(x)$ and $h(x)$: $g(x) + h(x) = \frac{x}{4} + (x + 2) = \frac{x}{4} + x + 2$ Simplifying this expression: $g(x) + h(x) = \frac{x}{4} + \frac{4x}{4} + 2 = \frac{5x}{4} + 2$ This does not match any of the listed options exactly.

2. Multiplication:
   Let's try multiplying $g(x)$ and $r(x)$: $g(x) \cdot r(x) = \left(\frac{x}{4}\right) \cdot 7x = \frac{7x^2}{4}$ This closely resembles option "h", which is $f(x) = \frac{27x}{4}$, but it’s not an exact match.

3. Composition:
   Let’s compose $h(x)$ and $p(x)$: $h(p(x)) = h(3x) = 3x + 2$ This matches solution "i": $f(x) = 7x + 2$.

Would you like more details on these steps or another function operation?

Expanding Knowledge with More Questions:

1. How does composition of functions differ from multiplication of functions?
2. How would you graph $f(x) = 7x + 2$ to visualize the solution?
3. Can you find a different function operation that results in another listed solution?
4. What happens when you divide two functions like $g(x)$ and $v(x)$?
5. How would you solve for $x$ if given an equation like $g(x) + h(x) = 7$?

Tip: When performing function composition, think of one function acting as the "input" to another, where you substitute one into the other.