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.