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Chapter 1: Problem 6
A graphical test for the existence of an inverse function of \(f\) is called the _____ Line Test.
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(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 \(f^{-1}\). $$ f(x)=-\frac{2}{x} $$
State sales tax is based on retail price. An item that sells for $$\$ 189.99$$ has a sales tax of $$\$ 11.40 .$$ Find a mathematical model that gives the amount of sales tax \(y\) in terms of the retail price \(x .\) Use the model to find the sales tax on a \(\$ 639.99\) purchase.
Assume that \(y\) is directly proportional to \(x\). Use the given \(x\) -value and \(y\) -value to find a linear model that relates \(y\) and \(x\). $$ x=6, y=580 $$
Use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ \left(f^{-1} \circ f^{-1}\right)(6) $$
Determine if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The number of miles \(n\) a marathon runner has completed in terms of the time \(t\) in hours
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