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Chapter 0: Problem 50
\(f(x)=x^{2}-8 x+15\)
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True or False? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer. $$ \text { If } f \text { is an even function, } f^{-1} \text { exists. } $$
Maximum Profit The cost per unit in the production of a portable CD player is \(\$ 60\). The manufacturer charges \(\$ 90\) per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by \(\$ 0.15\) per CD player for each unit ordered in excess of 100 (for example, there would be a charge of \(\$ 87\) per CD player for an order size of 120 ). (a) The table shows the profit \(P\) (in dollars) for various numbers of units ordered, \(x\). Use the table to estimate the maximum profit. \begin{tabular}{|l|c|c|c|c|} \hline Units, \(x\) & 110 & 120 & 130 & 140 \\ \hline Profit, \(P\) & 3135 & 3240 & 3315 & 3360 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|} \hline Units, \(x\) & 150 & 160 & 170 \\ \hline Profit, \(P\) & 3375 & 3360 & 3315 \\ \hline \end{tabular} (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x\) ? (c) If \(P\) is a function of \(x\), write the function and determine its domain.
The function given by
$$
y=0.03 x^{2}+245.50, \quad 0
In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=x^{2}-2, \quad x \leq 0 $$
In Exercises 69-74, use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ g^{-1} \circ f^{-1} $$
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