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Chapter 1: Problem 32
Find the zeros of the function algebraically. $$ f(x)=\sqrt{3 x+2} $$
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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 \(f^{-1}\). $$ f(x)=\frac{8 x-4}{2 x+6} $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ g(x)=\frac{x}{8} $$
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 \(x\). $$ x=5, y=12 $$
Use the functions given by \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$ f^{-1} \circ g^{-1} $$
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