Answer :
To find the inverse of the function defined by the given table, we need to swap the roles of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. In other words, the values that were originally associated with [tex]\(x\)[/tex] will now be associated with [tex]\(y\)[/tex], and vice versa. Let's go through the steps:
1. Understand the Original Function:
- The table given is:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 7 & 10 & 13 & 16 \\
\hline
$y$ & 21 & 30 & 39 & 48 \\
\hline
\end{tabular}
\][/tex]
```
- This tells us that when [tex]\(x = 7\)[/tex], [tex]\(y = 21\)[/tex], when [tex]\(x = 10\)[/tex], [tex]\(y = 30\)[/tex], and so on.
2. Build the Inverse Table:
- To create the inverse function, simply swap each [tex]\(x\)[/tex] value with its corresponding [tex]\(y\)[/tex] value:
- [tex]\(x\)[/tex] becomes [tex]\(y\)[/tex] and [tex]\(y\)[/tex] becomes [tex]\(x\)[/tex].
3. Generate the Inverse Table:
- The new inverse table will be:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 21 & 30 & 39 & 48 \\
\hline
$y$ & 7 & 10 & 13 & 16 \\
\hline
\end{tabular}
\][/tex]
```
4. Select the Correct Option:
- When we look at the options provided, the table that matches this inverse is:
- Option C:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 21 & 30 & 39 & 48 \\
\hline
$y$ & 7 & 10 & 13 & 16 \\
\hline
\end{tabular}
\][/tex]
```
So, the correct answer is Option C.
1. Understand the Original Function:
- The table given is:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 7 & 10 & 13 & 16 \\
\hline
$y$ & 21 & 30 & 39 & 48 \\
\hline
\end{tabular}
\][/tex]
```
- This tells us that when [tex]\(x = 7\)[/tex], [tex]\(y = 21\)[/tex], when [tex]\(x = 10\)[/tex], [tex]\(y = 30\)[/tex], and so on.
2. Build the Inverse Table:
- To create the inverse function, simply swap each [tex]\(x\)[/tex] value with its corresponding [tex]\(y\)[/tex] value:
- [tex]\(x\)[/tex] becomes [tex]\(y\)[/tex] and [tex]\(y\)[/tex] becomes [tex]\(x\)[/tex].
3. Generate the Inverse Table:
- The new inverse table will be:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 21 & 30 & 39 & 48 \\
\hline
$y$ & 7 & 10 & 13 & 16 \\
\hline
\end{tabular}
\][/tex]
```
4. Select the Correct Option:
- When we look at the options provided, the table that matches this inverse is:
- Option C:
```
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 21 & 30 & 39 & 48 \\
\hline
$y$ & 7 & 10 & 13 & 16 \\
\hline
\end{tabular}
\][/tex]
```
So, the correct answer is Option C.
