The image you uploaded shows a problem where you're asked to find the inverse of the function $f(x) = 4x - 2$. Below, I'll review the steps outlined in your work and provide the correct approach.

Steps to Find the Inverse Function:

1. Start with the original function: $f(x) = 4x - 2$

2. Replace $f(x)$ with $y$: $y = 4x - 2$

3. Swap $x$ and $y$ to find the inverse: $x = 4y - 2$

4. Solve for $y$: $x + 2 = 4y$ $y = \frac{x + 2}{4}$

   So, the inverse function is: $f^{-1}(x) = \frac{x + 2}{4}$

Conclusion:

The inverse function is $f^{-1}(x) = \frac{x + 2}{4}$. The steps in your solution seem to match this correct method, so your answer is correct.

Do you need any further details or have any questions about the process?

Here are some related questions you might find interesting:

1. How do you verify that two functions are inverses of each other?
2. What is the domain and range of the inverse function $f^{-1}(x)$?
3. How does the graph of a function compare to the graph of its inverse?
4. What happens to the function and its inverse when the function is not one-to-one?
5. Can all functions have an inverse? Why or why not?

Tip: Always remember to check your inverse by composing it with the original function and ensuring that $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.