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In this problem, the graph of a function \( f \) is provided, and you're asked to find the values of the inverse function \( f^{-1} \) at specific points.

For inverse functions, recall that if \( f(a) = b \), then \( f^{-1}(b) = a \). In other words, the inverse function swaps the roles of \( x \) and \( y \). Thus, to solve for \( f^{-1}(2) \), \( f^{-1}(4) \), and \( f^{-1}(5) \), you need to find where the original function \( f(x) \) equals 2, 4, and 5 respectively, and determine the corresponding \( x \)-values.

Let's go through each part:

1. **(a) \( f^{-1}(2) \)**:
   - Look for the \( x \)-value where \( f(x) = 2 \). From the graph, when \( f(x) = 2 \), the corresponding \( x \)-value is around **2**.
   
2. **(b) \( f^{-1}(4) \)**:
   - Find the \( x \)-value where \( f(x) = 4 \). According to the graph, \( f(x) = 4 \) occurs at \( x = 0 \), so \( f^{-1}(4) = 0 \).

3. **(c) \( f^{-1}(5) \)**:
   - Look for the \( x \)-value where \( f(x) = 5 \). The graph doesn't quite reach \( y = 5 \), so this value does not exist in the range of the graph.

Here are the answers:

- \( f^{-1}(2) = 2 \)
- \( f^{-1}(4) = 0 \)
- \( f^{-1}(5) \) does not exist in the graph's range.

Would you like a more detailed explanation? 

### Related Questions:
1. What are the key characteristics of an inverse function?
2. How can you determine if a function is one-to-one from its graph?
3. What is the graphical interpretation of the inverse function?
4. How does the range of a function affect the existence of its inverse values?
5. How can you verify whether a point lies on the graph of the inverse function?

### Tip:
When working with inverse functions graphically, remember that their graphs are reflections over the line \( y = x \).

A graph of a function is given. Use the graph to find the indicated inverse values: f^{-1}(2), f^{-1}(4), and f^{-1}(5).

Learn how to find the inverse of a function using its graph. This problem covers key concepts of inverse functions, graph interpretation, and their relationships. Suitable for students in Grades 10-12.

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