We are given a table for the function $g(x)$. We need to find $g(2)$ and $g^{-1}(\frac{1}{8})$.

1. Problem Description

We are given a table for the function $g(x)$. We need to find $g(2)$ and $g^{-1}(\frac{1}{8})$.

2. Solution Steps

First, we need to find $g(2)$. We look at the table and find the value of $g(x)$ when $x=2$. From the table, we see that when $x=2$, $g(2) = \frac{1}{2}$.

Next, we need to find $g^{-1}(\frac{1}{8})$. This means we are looking for the value of $x$ such that $g(x) = \frac{1}{8}$. From the table, we see that when $x=3$, $g(3) = \frac{1}{8}$. Therefore, $g^{-1}(\frac{1}{8}) = 3$.

3. Final Answer

$g(2) = \frac{1}{2}$

$g^{-1}(\frac{1}{8}) = 3$