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To find \( f(-4) \) from the given table of values for \( f^{-1} \):

The table shows values of \( f^{-1}(x) \), which is the inverse of \( f(x) \). We need to recall that if \( f^{-1}(x) = y \), then \( f(y) = x \). In this problem:

1. We want \( f(-4) \).
2. Looking at the table, \( f^{-1}(8) = -4 \).
3. By the definition of an inverse function, if \( f^{-1}(8) = -4 \), then \( f(-4) = 8 \).

So, the answer is:
\[
f(-4) = 8
\]

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### Related Questions
1. How do you determine if a function has an inverse?
2. What are the properties of inverse functions?
3. How do you interpret a function’s inverse graphically?
4. Can every function have an inverse?
5. How can you verify if two functions are inverses of each other?

### Tip
When working with inverse functions, remember that switching the \( x \) and \( y \) values in the original function gives you the inverse function's values.

Find f(-4) given the table of values for the inverse function f⁻¹(x).

Learn how to find f(-4) by analyzing a table of values for the inverse function f⁻¹(x). Understand the concept of inverse functions and function notation in this example suitable for high school students.

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