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The function \( g \) is the inverse of the function \( f \). By definition, if \( g \) is the inverse of \( f \), then:

\[
g(f(x)) = x \quad \text{and} \quad f(g(x)) = x
\]

To find \( g(2) \), we need to identify the input \( x \) such that \( f(x) = 2 \). From the table, we can see that when \( x = 4 \), \( f(4) = 2 \).

Therefore:

\[
g(2) = 4
\]

The answer is \( g(2) = 4 \).

Would you like more details or have any other questions? Here are some related questions to deepen your understanding:

1. What is the inverse function concept in mathematical terms?
2. How would you find \( g(-6) \) using the same table?
3. If \( g \) is the inverse of \( f \), how would you describe the graph of \( g \) compared to \( f \)?
4. What are the properties of invertible functions?
5. How can we verify that a function is invertible?

**Tip:** Remember, the inverse of a function swaps the roles of \( x \) and \( y \), meaning the inputs and outputs are reversed!

The function g is the inverse of f. What is g(2)?

Learn how to find g(2) when given the inverse of function f(x) using a table of values. This problem covers the inverse function theorem and function evaluation, ideal for high school students in Grades 9-12.

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