To find the inverse of the given functions, we'll follow the standard steps. Let's handle each function separately:

1. Inverse of $m(x) = 7x - 5$

Step-by-Step Process:

1. Replace $m(x)$ with $y$:
   $y = 7x - 5$

2. Swap $x$ and $y$ (this is the key step to finding the inverse):
   $x = 7y - 5$

3. Solve for $y$:
   Add 5 to both sides:
   $x + 5 = 7y$
   Now divide both sides by 7:
   $y = \frac{x + 5}{7}$

4. Replace $y$ with $m^{-1}(x)$ to denote the inverse function:
   $m^{-1}(x) = \frac{x + 5}{7}$

So, the inverse of $m(x) = 7x - 5$ is $m^{-1}(x) = \frac{x + 5}{7}$.

2. Inverse of $f(x) = 3x - 8$

Step-by-Step Process:

1. Replace $f(x)$ with $y$:
   $y = 3x - 8$

2. Swap $x$ and $y$:
   $x = 3y - 8$

3. Solve for $y$:
   Add 8 to both sides:
   $x + 8 = 3y$
   Now divide both sides by 3:
   $y = \frac{x + 8}{3}$

4. Replace $y$ with $f^{-1}(x)$ to denote the inverse function:
   $f^{-1}(x) = \frac{x + 8}{3}$

So, the inverse of $f(x) = 3x - 8$ is $f^{-1}(x) = \frac{x + 8}{3}$.

Would you like a detailed breakdown of any of these steps? Here are five follow-up questions:

1. What are the four steps involved in finding the inverse of a function?
2. How can you verify that two functions are inverses of each other?
3. Why do we swap $x$ and $y$ when finding the inverse?
4. How does the slope of the original function compare with its inverse?
5. What is the general form of an inverse for a linear function $f(x) = ax + b$?

Tip: Always remember to check your work by plugging the inverse function back into the original function. If $f(f^{-1}(x)) = x$, then you have found the correct inverse.