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The problem asks for the value of \( f^{-1}(-2) \), where \( f^{-1}(x) \) is the inverse function of \( f(x) \). This means we need to find the \( x \)-value such that \( f(x) = -2 \). 

Looking at the table provided:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 2 \\
-1 & 6 \\
0 & 10 \\
1 & 14 \\
2 & 18 \\
\hline
\end{array}
\]

None of the \( y \)-values in the table match \(-2\), so this means \( f(x) = -2 \) is not possible for any of the listed \( x \)-values. Therefore, \( f^{-1}(-2) \) does not exist.

Would you like more details on inverse functions or related concepts? 

Here are five questions that expand on this:

1. What are the conditions for a function to have an inverse?
2. How do you find the inverse of a function algebraically?
3. How do you graph the inverse of a function?
4. What does it mean when an inverse function doesn't exist?
5. How do you verify if two functions are inverses of each other?

**Tip:** When looking for the inverse of a function, swap the \( x \)- and \( y \)-coordinates, then solve for \( x \).

Explore how to determine whether an inverse function exists using a function table. This problem demonstrates the process of finding f^(-1)(-2) and understanding when an inverse does not exist. Suitable for students in Grades 9-12.

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