The image shows a graph of a function $f$, and a question is asked whether $f$ has an inverse. You correctly indicated "Yes" because the graph passes the horizontal line test (no horizontal line intersects the graph at more than one point), meaning $f$ is one-to-one and thus has an inverse.

The problem also asks for the values of the inverse function $f^{-1}(-1)$ and $f^{-1}(7)$. Here's how to analyze these:

1. For $f^{-1}(-1)$:

   • $f^{-1}(-1) = 2$ is correct. This means that $f(2) = -1$, which matches the graph where $f(2) = -1$.

2. For $f^{-1}(7)$:

   • You entered "DNE" (Does Not Exist) for $f^{-1}(7)$, but this was marked incorrect. To clarify, this means that the function $f$ does not reach 7 on the $y$-axis within the domain shown in the graph. So it seems your understanding was right, but the system expected a different response. Possibly, the expected value might be based on interpreting $f(3)$ or some error in input handling.

Let me know if you'd like further clarification or if you want to explore the inverse functions in more detail!

Relative Questions:

1. What does it mean for a function to have an inverse?
2. How can we apply the horizontal line test to determine if a function is invertible?
3. What are the typical notations for expressing inverse functions?
4. How can you determine the inverse of a function from its graph?
5. Why would $f^{-1}(7)$ be labeled as incorrect in this context?

Tip:

When solving for the inverse of a function graphically, always ensure that the $y$-values match points on the graph for that specific domain.