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From the graph you provided, the task is to find the values of \( f^{-1}(x) \) for different values of \( x \). The function \( f^{-1}(x) \) is the inverse of \( f(x) \), which means that if \( f(a) = b \), then \( f^{-1}(b) = a \).

To solve this, we will reverse the roles of the \( x \)- and \( y \)-coordinates from the graph of \( f(x) \). Here's how we can approach it based on the graph:

1. **\( f^{-1}(-4) \)**: 
   Look at the graph for where \( f(x) = -4 \) and find the corresponding \( x \)-value. From the graph, this appears to occur at \( x = -7 \). Therefore, \( f^{-1}(-4) = -7 \).

2. **\( f^{-1}(-3) \)**: 
   Look for the point where \( f(x) = -3 \). From the graph, it looks like this happens at \( x = -6 \). So, \( f^{-1}(-3) = -6 \).

3. **\( f^{-1}(0) \)**: 
   Look where \( f(x) = 0 \). The graph shows that this happens at \( x = -2 \). Thus, \( f^{-1}(0) = -2 \).

4. **\( f^{-1}(2) \)**: 
   Find where \( f(x) = 2 \). According to the graph, this happens at \( x = 0 \). Therefore, \( f^{-1}(2) = 0 \).

5. **\( f^{-1}(4) \)**: 
   Look for where \( f(x) = 4 \). The graph shows that this happens at \( x = 1 \). Thus, \( f^{-1}(4) = 1 \).

Here is the summary of the answers:
1. \( f^{-1}(-4) = -7 \)
2. \( f^{-1}(-3) = -6 \)
3. \( f^{-1}(0) = -2 \)
4. \( f^{-1}(2) = 0 \)
5. \( f^{-1}(4) = 1 \)

Let me know if you would like any further explanation or details!

Here are 5 related questions for deeper understanding:
1. How do you find the inverse of a function algebraically?
2. What does the symmetry of a function and its inverse around the line \( y = x \) mean?
3. How would you graph \( f^{-1}(x) \) if you were only given the graph of \( f(x) \)?
4. Why is it important for a function to be one-to-one for its inverse to exist?
5. Can a function have an inverse if it is not continuous?

**Tip:** Remember that the graph of a function and its inverse are reflections over the line \( y = x \).

Use the given graph of the function f to find the following values for f^{-1}: f^{-1}(-4), f^{-1}(-3), f^{-1}(0), f^{-1}(2), f^{-1}(4).

Learn how to use a given graph to find values of an inverse function. This exercise involves interpreting graph coordinates and applying the inverse function relationship: f(a) = b implies f^{-1}(b) = a.

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