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Chapter 1: Problem 25
Evaluate the indicated function for \(f(x)=x^{2}+1\) and \(g(x)=x-4\). $$ (f / g)(5) $$
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Use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ g^{-1} \circ f^{-1} $$
Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=2 $$
(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 \(f^{-1}\). $$ f(x)=\frac{6 x+4}{4 x+5} $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ h(x)=-\frac{4}{x^{2}} $$
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.
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