To solve this problem, we need to identify two points that lie on the graph of the inverse function [tex]\( f^{-1}(x) \)[/tex].
Given the table of values for [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{tabular}{|r|r|}
\hline
$x$ & $f(x)$ \\
\hline
-1 & 7 \\
\hline
1 & 6 \\
\hline
3 & 5 \\
\hline
4 & 1 \\
\hline
6 & -1 \\
\hline
\end{tabular}
\][/tex]
For any given point [tex]\((a, b)\)[/tex] on the function [tex]\( f(x) \)[/tex], the corresponding point [tex]\((b, a)\)[/tex] will lie on the inverse function [tex]\( f^{-1}(x) \)[/tex].
From the table, one known point on [tex]\( f(x) \)[/tex] is [tex]\((x, f(x)) = (-1, 7)\)[/tex]. The corresponding point on [tex]\( f^{-1}(x) \)[/tex] will be [tex]\((7, -1)\)[/tex].
To find another point, we can simply choose another pair from the table. Let's choose [tex]\((1, 6)\)[/tex]. The corresponding point on [tex]\( f^{-1}(x) \)[/tex] will be [tex]\((6, 1)\)[/tex].
Thus, two points that lie on the graph of [tex]\( f^{-1}(x) \)[/tex] are:
[tex]\[
(7, -1) \text{ and } (6, 1)
\][/tex]
So, the correct answer for the second point is [tex]\((6, 1)\)[/tex].
