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Chapter 0: Problem 33
Solve the equation and check your solution. (If not possible, explain why.) $$ 10-\frac{13}{x}=4+\frac{5}{x} $$
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In Exercises 33-38, use a graphing utility to graph the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $$ g(x)=(x+5)^{3} $$
In Exercises 27 and 28, use the table of values for \(y=f(x)\) to complete a table for \(y=f^{-1}(x)\). $$ \begin{array}{|l|r|r|r|r|r|r|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -10 & -7 & -4 & -1 & 2 & 5 \\ \hline \end{array} $$
In Exercises 55-68, determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=x^{4} $$
Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\). $$ \begin{array}{cc} \text { Function } & x \text {-Values } \\ f(x)=-x^{3}+6 x^{2}+x &\quad x_{1}=1, x_{2}=6 \end{array} $$
In Exercises 75-78, use the functions given by \(f(x)=x+4\) and \(g(x)=2 x-5\) to find the specified function. $$ (g \circ f)^{-1} $$
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