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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!

Learn how to find the inverse of the linear function f(x) = 2x + 5. This solution provides a step-by-step process suitable for high school students, focusing on inverse functions and algebraic manipulation.

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