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Chapter 1: Problem 23
Evaluate the indicated function for \(f(x)=x^{2}+1\) and \(g(x)=x-4\). $$ (f g)(6) $$
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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 \(f^{-1}\). $$ f(x)=\sqrt[3]{x-1} $$
Use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ \left(g^{-1} \circ g^{-1}\right)(-4) $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=x^{4} $$
Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=1 $$
Your wage is \(\$ 10.00\) per hour plus \(\$ 0.75\) for each unit produced per hour. So, your hourly wage \(y\) in terms of the number of units produced \(x\) is \(y=10+0.75 x\) (a) Find the inverse function. What does each variable represent in the inverse function? (b) Determine the number of units produced when your hourly wage is \(\$ 24.25\).
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