The table shows several points for the function [tex]j(t)[/tex].

\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] & 1 & 8 & 10 & 17 \\
\hline
[tex]$j(t)$[/tex] & 1 & 2 & 10 & 250 \\
\hline
\end{tabular}

Which table shows points for the inverse function [tex]j^{-1}(t)[/tex]?

A.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] & 1 & 8 & 10 & 17 \\
\hline
[tex]$j^{-1}(t)$[/tex] & -1 & -2 & -10 & -250 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] & 1 & 8 & 10 & 17 \\
\hline
[tex]$j^{-1}(t)$[/tex] & 1 & 0.5 & 0.1 & 0.004 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] & 1 & 2 & 10 & 250 \\
\hline
[tex]$j^{-1}(t)$[/tex] & 1 & 0.5 & 0.1 & 0.004 \\
\hline
\end{tabular}

D.
\begin{tabular}{|l|l|l|l|l|}
\hline
[tex]$t$[/tex] & 1 & 2 & 10 & 250 \\
\hline
\end{tabular}



Answer :

To solve for the points of the inverse function \( j^{-1}(t) \), we need to understand what an inverse function does. An inverse function essentially reverses the roles of \( t \) and \( j(t) \).

In other words, if \( j(t) = y \), then \( j^{-1}(y) = t \).

Given the table for \( j(t) \):
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline t & 1 & 8 & 10 & 17 \\ \hline j(t) & 1 & 2 & 10 & 250 \\ \hline \end{tabular} \][/tex]

We swap the input \( t \) and the output \( j(t) \) to find the points for the inverse function \( j^{-1}(t) \):

The new table for \( j^{-1}(t) \) would be:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline t & 1 & 2 & 10 & 250 \\ \hline j^{-1}(t) & 1 & 8 & 10 & 17 \\ \hline \end{tabular} \][/tex]

Thus, the correct option that displays the points for the inverse function \( j^{-1}(t) \) is:

[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline t & 1 & 2 & 10 & 250 \\ \hline j^{-1}(t) & 1 & 8 & 10 & 17 \\ \hline \end{tabular} \][/tex]