We are given the function $f(x) = 4x - 3$, and we are tasked with finding its inverse, denoted as $f^{-1}(x)$.

Steps to find the inverse:

1. Start with the equation:
   $y = f(x) = 4x - 3$

2. Solve for $x$ in terms of $y$:
   $y = 4x - 3$
   Add 3 to both sides:
   $y + 3 = 4x$
   Now divide by 4:
   $x = \frac{y + 3}{4}$

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

Thus, the inverse function is $f^{-1}(x) = \frac{x + 3}{4}$.

Correct answer:

A. $\frac{x + 3}{4}$

Would you like further clarification or more examples of finding inverse functions?

Follow-up questions:

1. How do you find the inverse of a function when it involves fractions or more complex operations?
2. What is the importance of the domain and range when dealing with inverse functions?
3. How can you check if two functions are inverses of each other?
4. How do you graph a function and its inverse on the same coordinate plane?
5. What is the relationship between the graph of a function and its inverse?

Tip: Always check if the function is one-to-one (i.e., it passes the horizontal line test) before finding its inverse. If it's not one-to-one, it doesn't have an inverse over its entire domain.