The question asks for the inverse functions of the given functions. Let's solve them one by one:

1. f(x) = 3x - 7

   • To find the inverse, swap $x$ and $y$ in the equation: $y = 3x - 7$ Swap $x$ and $y$: $x = 3y - 7$ Solve for $y$: $x + 7 = 3y \implies y = \frac{x + 7}{3}$ Therefore, the inverse function is: $f^{-1}(x) = \frac{x + 7}{3}$

2. g(x) = 9 - 2x

   • Start by swapping $x$ and $y$: $y = 9 - 2x$ Swap $x$ and $y$: $x = 9 - 2y$ Solve for $y$: $2y = 9 - x \implies y = \frac{9 - x}{2}$ Therefore, the inverse function is: $g^{-1}(x) = \frac{9 - x}{2}$

3. h(x) = \frac{1}{4}x + 5

   • Swap $x$ and $y$: $y = \frac{1}{4}x + 5$ Swap $x$ and $y$: $x = \frac{1}{4}y + 5$ Solve for $y$: $x - 5 = \frac{1}{4}y \implies y = 4(x - 5)$ Therefore, the inverse function is: $h^{-1}(x) = 4(x - 5)$

4. k(x) = 2 - \frac{1}{5}x

   • Swap $x$ and $y$: $y = 2 - \frac{1}{5}x$ Swap $x$ and $y$: $x = 2 - \frac{1}{5}y$ Solve for $y$: $\frac{1}{5}y = 2 - x \implies y = 5(2 - x)$ Therefore, the inverse function is: $k^{-1}(x) = 5(2 - x)$

Do you want more details, or do you have any questions?

Here are five related questions for you to consider:

1. How can you verify if a function is one-to-one before finding its inverse?
2. What is the graphical relationship between a function and its inverse?
3. Can all functions have an inverse? If not, why?
4. How can you use the horizontal line test to check if a function has an inverse?
5. What happens to the domain and range of a function when you find its inverse?

Tip: To check if your inverse function is correct, compose the original and inverse functions. The result should be $x$.