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Let's find the inverse function \( f^{-1}(x) \) for the given function \( f(x) = 2x + 4 \).

### Step-by-Step Solution:

1. Start with the function \( f(x) = 2x + 4 \).
   
2. To find the inverse, we replace \( f(x) \) with \( y \):
   \[
   y = 2x + 4
   \]
   
3. Swap \( x \) and \( y \) to begin solving for \( y \):
   \[
   x = 2y + 4
   \]
   
4. Now, solve for \( y \):
   \[
   x - 4 = 2y
   \]
   \[
   y = \frac{x - 4}{2}
   \]
   
5. Therefore, the inverse function is:
   \[
   f^{-1}(x) = \frac{x - 4}{2}
   \]

### Conclusion:
The correct answer is option **B**: \( f^{-1}(x) = \frac{x - 4}{2} \).

Would you like further details on this or have any other questions?

Here are some related questions you might consider:
1. How do you verify that two functions are inverses of each other?
2. What are the general steps for finding an inverse function?
3. What is the domain and range of the function \( f(x) = 2x + 4 \)?
4. How do inverse functions behave graphically with respect to the line \( y = x \)?
5. How can you find the inverse of a quadratic function?

**Tip**: When solving for an inverse, always remember to swap \( x \) and \( y \), and then solve for \( y \).

Learn how to find the inverse of the linear function f(x) = 2x + 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inverse functions and solving linear equations. Suitable for students in Grades 9-12.

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