Select the correct answer from each drop-down menu.

\begin{tabular}{|r|r|}
\hline[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline-1 & 7 \\
\hline 1 & 6 \\
\hline 3 & 5 \\
\hline 4 & 1 \\
\hline 6 & -1 \\
\hline
\end{tabular}

The values in the table define the function [tex]$f(x)$[/tex]. Two points that lie on the graph of [tex]$f^{-1}(x)$[/tex] are [tex]$\square$[/tex] and [tex]$\square$[/tex].



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]