To find the inverse of the function $f(x) = 2x + 5$, we follow these steps:

1. Replace $f(x)$ with $y$: $y = 2x + 5$

2. Swap $x$ and $y$ to find the inverse: $x = 2y + 5$

3. Solve for $y$ (which is the inverse function): $x - 5 = 2y$ $y = \frac{x - 5}{2}$

Thus, the inverse function is: $f^{-1}(x) = \frac{x - 5}{2}$

Now let's check the options:

• Option C: $f^{-1}(x) = \frac{x - 5}{2}$ is the correct answer.

Would you like more details on inverse functions or how to verify the result?

Here are 5 related questions for deeper understanding:

1. How can you verify if two functions are inverses of each other?
2. What happens graphically when you plot a function and its inverse?
3. Can every function have an inverse? Why or why not?
4. How do you find the inverse of a quadratic function?
5. What is the significance of the horizontal line test in determining inverses?

Tip: When finding inverses, always remember to swap $x$ and $y$, then solve for $y$ again to find the inverse function!