91Ó°ÊÓ

Determine whether the inverse of \(f\) is a function. Then find the inverse. $$f(x)=\frac{3}{x}-2$$

In Exercises 39-44, simplify the complex fraction. \(\frac{\frac{x}{3}-6}{10+\frac{4}{x}}\)

In Exercises 33-40, rewrite the function in the form \(g(x)=\frac{a}{x-h}+k\). Graph the function. Describe the graph of \(g\) as a transformation of the graph of \(f(x)=\frac{a}{x}\). $$ g(x)=\frac{7 x-20}{x+13} $$

Determine whether the inverse of \(f\) is a function. Then find the inverse. $$f(x)=\frac{5}{x}-6$$

In Exercises 33-40, rewrite the function in the form \(g(x)=\frac{a}{x-h}+k\). Graph the function. Describe the graph of \(g\) as a transformation of the graph of \(f(x)=\frac{a}{x}\). $$ g(x)=\frac{9 x-3}{x+7} $$

Simplify the complex fraction. \(\frac{15-\frac{2}{x}}{\frac{x}{5}+4}\)

Complete the table for the function \(y=\frac{x+4}{x^2-16}\) Then use the trace feature of a graphing calculator to explain the behavior of the function at x = ?4. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline-3.5 & \\ \hline-3.8 & \\ \hline-3.9 & \\ \hline-4.1 & \\ \hline-4.2 & \\ \hline \end{array} $$

Your school purchases a math software program. The program has an initial cost of $$\$ 500$$ plus $$\$ 20$$ for each student that uses the program. (See Example 5.) a. Estimate how many students must use the program for the average cost per student to fall to \(\$ 30\). b. What happens to the average cost as more students use the program?

Simplify the complex fraction. \(\frac{\frac{1}{2 x-5}-\frac{7}{8 x-20}}{\frac{x}{2 x-5}}\)

Determine whether the inverse of \(f\) is a function. Then find the inverse. $$f(x)=\frac{4}{11-2 x}$$