Use the given graph of the function ff to find the following values for f^−1

**1.** f^−1(−4)= 

**2.** f^−1(−3)=

**3.** f^−1(0)=

**4.** f^−1(2)=

**5.** f^6−1(4)=



To find the values for \( f^{-1}(x) \) using the graph of the function \( f(x) \), we need to understand that the inverse function \( f^{-1}(x) \) essentially swaps the roles of \( x \) and \( y \). In other words, if \( f(a) = b \), then \( f^{-1}(b) = a \).

Let's analyze the graph to answer each of the questions:

1. **\( f^{-1}(-4) \)**: We need to find the value of \( x \) such that \( f(x) = -4 \).
   - From the graph, when \( y = -4 \), the corresponding \( x \)-value is approximately \( x = 5 \).
   - So, \( f^{-1}(-4) = 5 \).

2. **\( f^{-1}(-3) \)**: We need to find the value of \( x \) such that \( f(x) = -3 \).
   - From the graph, when \( y = -3 \), the corresponding \( x \)-value is approximately \( x = 4 \).
   - So, \( f^{-1}(-3) = 4 \).

3. **\( f^{-1}(0) \)**: We need to find the value of \( x \) such that \( f(x) = 0 \).
   - From the graph, when \( y = 0 \), the corresponding \( x \)-value is approximately \( x = 1 \).
   - So, \( f^{-1}(0) = 1 \).

4. **\( f^{-1}(2) \)**: We need to find the value of \( x \) such that \( f(x) = 2 \).
   - From the graph, when \( y = 2 \), the corresponding \( x \)-value is approximately \( x = -1 \).
   - So, \( f^{-1}(2) = -1 \).

5. **\( f^{-1}(4) \)**: We need to find the value of \( x \) such that \( f(x) = 4 \).
   - From the graph, when \( y = 4 \), the corresponding \( x \)-value is approximately \( x = -3 \).
   - So, \( f^{-1}(4) = -3 \).

To summarize:
1. \( f^{-1}(-4) = 5 \)
2. \( f^{-1}(-3) = 4 \)
3. \( f^{-1}(0) = 1 \)
4. \( f^{-1}(2) = -1 \)
5. \( f^{-1}(4) = -3 \)

Would you like more details or have any questions about these calculations? Here are some related questions:

1. How do you find the inverse of a function algebraically?
2. What is the significance of the inverse function in real-world applications?
3. How can you graph the inverse of a function?
4. What are the conditions for a function to have an inverse?
5. How do you verify if two functions are inverses of each other?

**Tip:** When working with the inverse of a function, always check the original function's graph to ensure that the inverse values make sense within the given context.

Discover how to find inverse function values using the graph of the function. Explore solutions for specific values such as f^-1(-4), f^-1(-3), f^-1(0), f^-1(2), and f^-1(4) with detailed graphical analysis. Suitable for high school students and anyone learning about inverse functions and graphical interpretations.

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