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.