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Waterloo Park posted the following schedule listing the number of hours an employee works on a given day. Let [tex]$B(x)$[/tex], [tex]$T(x)$[/tex], [tex]$R(x)$[/tex], and [tex]$S(x)$[/tex] represent the number of hours worked by Bill, Ted, Rufus, and Socrates, respectively, on a given day [tex]$x$[/tex].

\begin{tabular}{|l|r|r|r|r|r|}
\hline
& Mon & Tues & Wed & Thurs & Fri \\
\hline
Bill & 6 & 5 & 4 & 7 & 8 \\
\hline
Ted & 4 & 0 & 6 & 10 & 3 \\
\hline
Rufus & 8 & 3 & 6 & 5 & 0 \\
\hline
Socrates & 1 & 2 & 3 & 4 & 0 \\
\hline
\end{tabular}

What is the value of the inverse shown below?
[tex]\[ S^{-1}(0)= \][/tex]
[tex]\[ \square \][/tex]



Answer :

GinnyAnswer
To find the value of [tex]\( S^{-1}(0) \)[/tex], we need to determine on which day Socrates worked 0 hours. We start by examining the schedule for Socrates:

[tex]\[ \begin{array}{|l|r|r|r|r|r|} \hline & \text{Mon} & \text{Tues} & \text{Wed} & \text{Thurs} & \text{Fri} \\ \hline \text{Socrates} & 1 & 2 & 3 & 4 & 0 \\ \hline \end{array} \][/tex]

From this schedule, we observe the number of hours Socrates worked each day:
- Monday: 1 hour
- Tuesday: 2 hours
- Wednesday: 3 hours
- Thursday: 4 hours
- Friday: 0 hours

We are interested in the day he worked 0 hours. Reviewing the schedule, Socrates worked 0 hours on Friday.

Therefore, the value of the inverse function [tex]\( S^{-1}(0) \)[/tex] is:

[tex]\[ S^{-1}(0) = \text{Friday} \][/tex]

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