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Chapter 1: Problem 31
Find the distance between the points. $$ (-2,6),(3,-6) $$
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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. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=2 $$
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 \(x\). $$ x=5, y=12 $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{x-2} $$
Use the functions given by \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$ (g \circ f)^{-1} $$
Use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ (f \circ g)^{-1} $$
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