Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Select the correct answer.

Consider the function.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & -1 & 0 & 1 & 2 \\
\hline[tex]$f(x)$[/tex] & -2 & 3 & 8 & 13 \\
\hline
\end{tabular}

Which function could be the inverse of the given function?

A.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & -1 & 0 & 1 & 2 \\
\hline[tex]$p(x)$[/tex] & 2 & -3 & -8 & -13 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & -2 & 3 & 8 & 13 \\
\hline[tex]$q(x)$[/tex] & -1 & 0 & 1 & 2 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 1 & 0 & -1 & -2 \\
\hline[tex]$s(x)$[/tex] & -2 & 3 & 8 & 13 \\
\hline
\end{tabular}

D.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 2 & -3 & -8 & -13 \\
\hline[tex]$r(x)$[/tex] & 1 & 0 & -1 & -2 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which function represents the inverse of the given function, we need to understand the concept of inverse functions. An inverse function essentially swaps the x and f(x) values of the original function.

Given the table for the function [tex]\(f(x)\)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 \\ \hline f(x) & -2 & 3 & 8 & 13 \\ \hline \end{array} \][/tex]

To find the inverse function, we switch the x and f(x) values:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -2 & 3 & 8 & 13 \\ \hline f^{-1}(x) & -1 & 0 & 1 & 2 \\ \hline \end{array} \][/tex]

Now, let's compare this table to the provided options:

A.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -1 & 0 & 1 & 2 \\ \hline p(x) & 2 & -3 & -8 & -13 \\ \hline \end{array} \][/tex]
Option A does not match our derived inverse table.

B.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -2 & 3 & 8 & 13 \\ \hline q(x) & -1 & 0 & 1 & 2 \\ \hline \end{array} \][/tex]
Option B matches our derived inverse table exactly.

C.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 0 & -1 & -2 \\ \hline s(x) & -2 & 3 & 8 & 13 \\ \hline \end{array} \][/tex]
Option C does not match our derived inverse table.

D.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 2 & -3 & -8 & -13 \\ \hline r(x) & 1 & 0 & -1 & -2 \\ \hline \end{array} \][/tex]
Option D does not match our derived inverse table.

Based on this, the correct option that represents the inverse of the given function is Option B.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.