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Chapter 0: Problem 37
Solve the equation and check your solution. (If not possible, explain why.) $$ \frac{x}{x+4}+\frac{4}{x+4}+2=0 $$
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In Exercises 69-74, use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ \left(f^{-1} \circ f^{-1}\right)(6) $$
(a) The sales tax on a purchased item is a function of the selling price. (b) Your score on the next algebra exam is a function of the number of hours you study the night before the exam.
In Exercises 39-54, (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 \(f^{-1}\). $$ f(x)=3 x+1 $$
In Exercises 55-68, determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=x^{4} $$
In Exercises 27 and 28, use the table of values for \(y=f(x)\) to complete a table for \(y=f^{-1}(x)\). $$ \begin{array}{|l|r|r|r|r|r|r|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline f(x) & -2 & 0 & 2 & 4 & 6 & 8 \\ \hline \end{array} $$
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