https://file.aiquickdraw.com/mathbot/file/1727478972982io2kxxjs.jpg

1. F^-1(-4) =
2.f^-1(-3)=
3.f^-1(0)=
4. F^-1(2)=
5. F^-1(4)=

Let's analyze the graph in your image to determine the inverse function values \( f^{-1}(x) \).

From the graph, we can find \( f^{-1}(x) \) by interpreting it as finding the x-value that corresponds to a given y-value on the graph of \( f(x) \).

Here’s how to determine each:

1. **\( f^{-1}(-4) \)**: Find the point on the graph where \( f(x) = -4 \). The corresponding x-value is \( f^{-1}(-4) \).
2. **\( f^{-1}(-3) \)**: Look for \( f(x) = -3 \), then find the corresponding x-value, which gives \( f^{-1}(-3) \).
3. **\( f^{-1}(0) \)**: When \( f(x) = 0 \), find the corresponding x-value to get \( f^{-1}(0) \).
4. **\( f^{-1}(2) \)**: For \( f(x) = 2 \), find the corresponding x-value, giving \( f^{-1}(2) \).
5. **\( f^{-1}(4) \)**: Locate where \( f(x) = 4 \), and find the corresponding x-value, resulting in \( f^{-1}(4) \).

Let me inspect the graph closely and determine these values.I've opened the image to analyze the graph more closely. Let's now determine the values for the inverse function \( f^{-1} \).

From the graph:

1. \( f(x) = -4 \) corresponds to \( x = -8 \), so \( f^{-1}(-4) = -8 \).
2. \( f(x) = -3 \) corresponds to \( x = -6 \), so \( f^{-1}(-3) = -6 \).
3. \( f(x) = 0 \) corresponds to \( x = -2 \), so \( f^{-1}(0) = -2 \).
4. \( f(x) = 2 \) corresponds to \( x = 1 \), so \( f^{-1}(2) = 1 \).
5. \( f(x) = 4 \) corresponds to \( x = 4 \), so \( f^{-1}(4) = 4 \).

The answers are:
- \( f^{-1}(-4) = -8 \)
- \( f^{-1}(-3) = -6 \)
- \( f^{-1}(0) = -2 \)
- \( f^{-1}(2) = 1 \)
- \( f^{-1}(4) = 4 \)

Would you like more details or explanations on how these values were determined?

Here are 5 related questions you might consider:
1. What is the graphical relationship between a function and its inverse?
2. How do you determine if a function is invertible from its graph?
3. Can all functions have inverses? Why or why not?
4. What does the graph of the inverse function \( f^{-1}(x) \) look like compared to \( f(x) \)?
5. How can you algebraically find the inverse of a function?

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

1. f^-1(-4) =
2. f^-1(-3) =
3. f^-1(0) =
4. f^-1(2) =
5. f^-1(4) =

Learn how to find inverse function values using a graph of f(x). This step-by-step solution teaches you how to interpret inverse values based on the graph, suitable for high school students. Explore key concepts like inverse functions and graph interpretation.

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