To determine which graph correctly shows the inverse of the given function $f$ (blue solid curve), let's go step by step:

Key Facts About Inverses:

1. The inverse function reflects the original graph across the line $y = x$.
2. The points $(x, y)$ on the original function map to $(y, x)$ on the inverse function.
3. Visually, the graph of the inverse will appear as if flipped over the diagonal line $y = x$.

Examining the Options:

1. Option A: The red dashed curve does not reflect properly across $y = x$. Rejected.
2. Option B: The red dashed curve appears to reflect correctly across $y = x$. Possible.
3. Option C: The red dashed curve is horizontal and not a proper reflection of the blue curve. Rejected.
4. Option D: The red dashed curve does not reflect correctly across $y = x$. Rejected.

Correct Answer:

Option B is the correct choice because the red dashed curve correctly shows the reflection of the blue solid curve across the line $y = x$.

Let me know if you'd like further clarification on how inverses work or how to identify them on graphs!

Related Questions:

1. How do you determine if a function is one-to-one?
2. What is the process for finding the inverse algebraically?
3. How does the line $y = x$ relate to inverses visually?
4. How can you verify if two functions are inverses of each other?
5. What is the importance of the horizontal line test in determining inverses?

Tip: Always check symmetry across the line $y = x$ to identify the inverse graph.