To find the points that lie on the graph of the inverse function [tex]\( f^{-1}(x) \)[/tex], we need to swap the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] coordinates of the points given for [tex]\( f(x) \)[/tex].
Given the table:
[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]
1. For the point [tex]\((-1, 7)\)[/tex] on [tex]\( f(x) \)[/tex], the corresponding point on [tex]\( f^{-1}(x) \)[/tex] is [tex]\((7, -1)\)[/tex].
2. For the point [tex]\((1, 6)\)[/tex] on [tex]\( f(x) \)[/tex], the corresponding point on [tex]\( f^{-1}(x) \)[/tex] is [tex]\((6, 1)\)[/tex].
3. For the point [tex]\((3, 5)\)[/tex] on [tex]\( f(x) \)[/tex], the corresponding point on [tex]\( f^{-1}(x) \)[/tex] is [tex]\((5, 3)\)[/tex].
4. For the point [tex]\((4, 1)\)[/tex] on [tex]\( f(x) \)[/tex], the corresponding point on [tex]\( f^{-1}(x) \)[/tex] is [tex]\((1, 4)\)[/tex].
5. For the point [tex]\((6, -1)\)[/tex] on [tex]\( f(x) \)[/tex], the corresponding point on [tex]\( f^{-1}(x) \)[/tex] is [tex]\((-1, 6)\)[/tex].
Choosing any two of these points that lie on the graph of [tex]\( f^{-1}(x) \)[/tex]:
[tex]\[
(7, -1)
\][/tex]
and
[tex]\[
(6, 1)
\][/tex]
