The problem asks for the inverse of the function $f(x) = \frac{3 - x}{5}$.

To find the inverse, follow these steps:

1. Start with the equation for $f(x)$: $y = \frac{3 - x}{5}$

2. Swap $x$ and $y$ to begin solving for the inverse: $x = \frac{3 - y}{5}$

3. Multiply both sides of the equation by 5 to eliminate the denominator: $5x = 3 - y$

4. Isolate $y$ by subtracting 3 from both sides: $5x - 3 = -y$

5. Multiply through by -1 to solve for $y$: $y = 3 - 5x$

Thus, the inverse function is $f^{-1}(x) = 3 - 5x$.

The correct answer is option D.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you verify if two functions are inverses of each other?
2. What is the general process to find an inverse function?
3. Can every function have an inverse? Why or why not?
4. How would the process differ if the function were not linear?
5. What is the geometric interpretation of an inverse function?

Tip: The graph of a function and its inverse are reflections of each other across the line $y = x$.