91Ó°ÊÓ

Determine whether each pair of functions \(f\) and \(g\) are inverses. Explain your reasoning. $$ \begin{aligned} &\text { a. }\\\ &\begin{array}{|l|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -2 & 1 & 4 & 7 & 10 \\ \hline \end{array}\\\ &\begin{array}{|l|c|c|c|c|c|} \hline x & -2 & 1 & 4 & 7 & 10 \\ \hline g(x) & -2 & -1 & 0 & 1 & 2 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { b. }\\\ &\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 8 & 6 & 4 & 2 & 0 \\ \hline \end{array}\\\ &\begin{array}{|l|c|c|c|c|c|} \hline x & 2 & 3 & 4 & 5 & 6 \\ \hline g(x) & -8 & -6 & -4 & -2 & 0 \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\text { c. }\\\ &\begin{array}{|l|c|c|c|c|c|} \hline x & -4 & -2 & 0 & 2 & 4 \\ \hline f(x) & 2 & 10 & 18 & 26 & 34 \\ \hline \end{array}\\\ &\begin{array}{|l|c|c|c|c|c|} \hline x & -4 & -2 & 0 & 2 & 4 \\ \hline g(x) & \frac{1}{2} & \frac{1}{10} & \frac{1}{18} & \frac{1}{26} & \frac{1}{34} \\ \hline \end{array} \end{aligned} $$

\(\sqrt[5]{288}\)

\(\frac{\sqrt[4]{4}}{\sqrt[4]{27}}\)

\(\sqrt[4]{\frac{1296}{25}}\)

Evaluate the expression using a calculator. Round your answer to two decimal places when appropriate. (See Example 3.) \(20,736^{4 / 5}\)

In Exercises 27–34, solve the equation. Check your solution(s). $$ 2 x^{3 / 4}-14=40 $$

\(\frac{2}{\sqrt{8}+\sqrt{7}}\)

The range of the function \(y=a \sqrt{x}\) is \(y \geq 0\).

The domain and range of the function \(y=\sqrt[3]{x-h}+k\) are all real numbers.

Let \(g\) be a vertical stretch by a factor of 2 , followed by a translation 2 units up of the graph of \(f(x)=\sqrt{x}+3\).