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To find the value of \( g^{-1}(2) \), we need to identify where \( g(x) = 2 \) in the given table. Since \( g^{-1}(y) \) represents the value of \( x \) such that \( g(x) = y \), we search the table for the input that corresponds to the output of 2.

Looking at the table:

\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-3 & -54 \\
-2 & -16 \\
-1 & -2 \\
0  & 0 \\
1  & 2 \\
2  & 16 \\
3  & 54 \\
\hline
\end{array}
\]

We see that \( g(1) = 2 \). Therefore:

\[
g^{-1}(2) = 1
\]

Would you like any further details on this, or have any additional questions?

Here are 5 related questions:
1. How do you verify if a function is one-to-one?
2. What is the difference between an inverse function and a reciprocal?
3. How do you graph the inverse of a function?
4. Can a function have more than one inverse?
5. How do you find the inverse of a function algebraically?

**Tip**: To check if a function is one-to-one, use the horizontal line test on its graph—if no horizontal line intersects the graph more than once, the function is one-to-one.

If g(x) is a one-to-one function, what is the value of g^(-1)(2)?

Learn how to find the inverse of a one-to-one function using a table of values. This problem walks you through finding g^(-1)(2) by identifying the corresponding x-value for g(x) = 2. Suitable for students in Grades 9-11.

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