To find the inverse of the function $f(x) = -3x + 5$, we need to follow these steps:

1. Rewrite the function by replacing $f(x)$ with $y$: $y = -3x + 5$

2. Swap $x$ and $y$ to begin finding the inverse: $x = -3y + 5$

3. Solve for $y$:

   • First, isolate the term involving $y$: $x - 5 = -3y$
   • Then, divide by $-3$: $y = -\frac{1}{3}x + \frac{5}{3}$

4. Rewrite $y$ as $f^{-1}(x)$: $f^{-1}(x) = -\frac{1}{3}x + \frac{5}{3}$

So, the correct answer is: $f^{-1}(x) = -\frac{1}{3}x + \frac{5}{3}$

This matches the second option in your list of choices.

Would you like further details on how the steps work, or do you have any questions?

Related Questions:

1. How do you verify if two functions are inverses of each other?
2. What are the key properties of inverse functions?
3. Can all functions have inverses? Why or why not?
4. How does the slope of the inverse compare to the original function?
5. What is the geometric interpretation of finding an inverse function?

Tip: When finding the inverse of a function, always remember to switch $x$ and $y$, then solve for $y$ again. This helps ensure accuracy.