91Ó°ÊÓ

Given that \(2^{y}=16^{x-3}\) and \(3^{y+2}=27^{x},\) find the value of \(x+y\)

Simplify. $$ \sqrt{192 x}-\sqrt{75 x} $$

Determine whether or not the given pairs of functions are inverses of each other. \(f(x)=2.5\left(x^{3}-7.1\right)\) \(g(x)=\sqrt[3]{0.4 x+7.1}\)

If \(x=\left(\log _{125} 5\right)^{\log _{5} 125},\) what is the value of \(\log _{3} x ?\)

For each function given below, (a) determine the domain and the range, (b) set an appropriate window, and (c) draw the graph. Graphs may vary, depending on the scale used. $$ f(x)=x \ln (x-2.1) $$

Match each function in Column A with its inverse from Column B. Column \(A\) (1) \(y=5 x^{3}+10\) (2) \(y=(5 x+10)^{3}\) (3) \(y=5(x+10)^{3}\) (4) \(y=(5 x)^{3}+10\) Column \(B\) A. \(y=\frac{\sqrt[3]{x}-10}{5}\) B. \(y=\sqrt[3]{\frac{x}{5}}-10\) C. \(y=\sqrt[3]{\frac{x-10}{5}}\) D. \(y=\frac{\sqrt[3]{x-10}}{5}\)

Simplify. $$ \frac{\sqrt[3]{24 x y^{8}}}{\sqrt[3]{3 x y}}[7.4] $$

For each function given below, (a) determine the domain and the range, (b) set an appropriate window, and (c) draw the graph. Graphs may vary, depending on the scale used. $$ f(x)=2 x^{3} \ln x $$

Simplify. $$ \frac{\sqrt[5]{a^{4} y^{6}}}{\sqrt{a y}} $$

Examine the following table. Is it possible that \(f\) and \(g\) are inverses of each other? Why or why not? \(\begin{array}{|r|r|r|}\hline x & {f(x)} & {g(x)} \\ \hline 6 & {6} & {6} \\\ {7} & {6.5} & {8} \\ {8} & {7} & {10} \\ {9} & {7.5} & {12} \\ {10} & {8} & {14} \\ {11} & {8.5} & {16} \\ {12} & {9} & {18} \\ \hline\end{array}\)