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To find \( f(-4) \) based on the given table of values for \( f^{-1} \), we need to understand the relationship between a function and its inverse. The value \( f(a) = b \) corresponds to \( f^{-1}(b) = a \).

In the table provided:

- \( x = 8 \) has \( f^{-1}(x) = -4 \).

This means:
\[
f(-4) = 8
\]

### Answer:
\[
f(-4) = 8
\]

Would you like a deeper explanation, or do you have any further questions?

Here are some related questions to consider:
1. How can we determine if a function has an inverse?
2. What are the steps to find the inverse of a function algebraically?
3. Why is it important that a function is one-to-one to have an inverse?
4. How would the table change if we were given values for \( f \) instead of \( f^{-1} \)?
5. How do you interpret the inverse function graphically?

**Tip:** Remember, if \( f(a) = b \), then \( f^{-1}(b) = a \), which is a key property when using tables for inverse functions.

Find f(-4) based on the given table of values for f^(-1).

Learn how to find f(-4) by using a table of inverse function values. This example demonstrates key concepts in algebra, focusing on the relationship between a function and its inverse. Suitable for high school students.

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