Question

waterloo park posted the following schedule listing the number of hours an employee works on a given day. let \\(b(x)\\), \\(t(x)\\), \\(r(x)\\), and \\(s(x)\\) represent the number of hours worked by bill, ted, rufus, and socrates, respectively, on a given day \\(x\\).

what is the value of the inverse shown below?
\\(s^{-1}(0) = \\)

Explanation:

Identify the function and target value

The problem asks for the value of \(S^{-1}(0)\), where \(S(x)\) represents the number of hours worked by Socrates on a given day \(x\).

Locate the data in the table

We look at the row labeled "Socrates" to find when the number of hours worked is \(0\):

• Monday: \(1\) hour
• Tuesday: \(2\) hours
• Wednesday: \(3\) hours
• Thursday: \(4\) hours
• Friday: \(0\) hours

Thus, \(S(\text{Friday}) = 0\).

Apply the definition of the inverse function

By definition of an inverse function, if \(S(x) = y\), then \(S^{-1}(y) = x\).
Since \(S(\text{Friday}) = 0\), we have:

$$ S^{-1}(0) = \text{Friday} $$

Answer:

• Tuesday
• Friday (Correct answer)
• Ted
• Rufus