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To determine the **domain** and **range** of the inverse function \( f^{-1}(x) \) from the graph of \( f(x) \), we need to remember that:

- The **domain** of \( f^{-1}(x) \) is the **range** of \( f(x) \).
- The **range** of \( f^{-1}(x) \) is the **domain** of \( f(x) \).

From the graph:

1. **Domain of \( f(x) \)**: The function starts at \( x = -4 \) and ends at \( x = 6 \). Hence, the domain of \( f(x) \) is:
   \[
   \text{Domain of } f(x) = [-4, 6]
   \]

2. **Range of \( f(x) \)**: The function ranges vertically from \( y = -4 \) to \( y = 6 \). Hence, the range of \( f(x) \) is:
   \[
   \text{Range of } f(x) = [-4, 6]
   \]

Thus, for the inverse function:

- **Domain of \( f^{-1}(x) \)** (which is the range of \( f(x) \)) is:
  \[
  \text{Domain of } f^{-1}(x) = [-4, 6]
  \]

- **Range of \( f^{-1}(x) \)** (which is the domain of \( f(x) \)) is:
  \[
  \text{Range of } f^{-1}(x) = [-4, 6]
  \]

These are the required answers in interval notation.

Let me know if you have any further questions or need additional details.

Here are five related questions:
1. How do you find the inverse of a function algebraically?
2. What are the conditions for a function to have an inverse?
3. Can the domain of a function ever include infinity?
4. What is the relationship between the graphs of a function and its inverse?
5. How would the graph of the inverse \( f^{-1}(x) \) look based on the given function?

**Tip**: When switching between a function and its inverse, remember to swap the x and y values!

The graph of f(x) is given. Determine the domain and range of f^{-1}(x) using interval notation.

Learn how to find the domain and range of an inverse function f^{-1}(x) from the graph of f(x). This example covers the relationship between a function and its inverse, focusing on switching x and y values for domain and range identification.

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