To solve the problem:

Step 1: Understand the task

We are given a function $f(x)$, which is invertible, and asked to find $f^{-1}(-7)$. This means we need to determine the value of $x$ such that $f(x) = -7$.

Step 2: Analyze the graph

Looking at the graph:

• The function $f(x)$ is a linear function (a straight line) that decreases as $x$ increases.
• We observe the yellow line $f(x)$, which intersects $y = -7$.

Step 3: Find the corresponding $x$

From the graph:

• The point where $f(x) = -7$ is visible. Tracing the line, it corresponds to $x = -3$.

Thus, $f^{-1}(-7) = -3$.

Would you like me to explain this in more depth or confirm further? Let me know!

Related Questions:

1. What does it mean for a function to be invertible?
2. How can you algebraically determine the inverse of a linear function?
3. What are the steps for verifying if a given point satisfies the inverse function?
4. How does the slope of the line affect the calculation of $f^{-1}(y)$?
5. How can you identify symmetry in the graph of $f(x)$ and $f^{-1}(x)$?

Tip:

For an invertible function, the graph of $f^{-1}(x)$ is the reflection of $f(x)$ across the line $y = x$.