Answer :
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]
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]