91Ó°ÊÓ

Graph each function. \(y=\sqrt[3]{x+5}\)

Let \(f(x)=9 x\) and \(g(x)=3 x .\) Find \((f \cdot g)(x)\) and \(\left(\frac{f}{g}\right)(x)\) and their domains.

Simplify each radical expression. Use absolute value symbols when needed. $$ \sqrt{x^{8} y^{18}} $$

Write each expression in exponential form. $$(\sqrt[3]{a})^{2}$$

Solve. Check for extraneous solutions. \(\sqrt{3 x+7}=x-1\)

Solve each square root equation by graphing. Round the answer to the nearest hundredth if necessary. If there is no solution, explain why. \(\sqrt{2 x-3}=4\)

Simplify each radical expression. Use absolute value symbols when needed. $$ \sqrt[4]{x^{8} y^{12}} $$

Geometry The formula for the volume of a sphere is \(V=\frac{4}{3} \pi r^{3} .\) a. Find the inverse of the formula. Is the inverse a function? b. Use the inverse to find the radius of a sphere that has a volume of \(35,000 \mathrm{ft}^{3}\) .

Solve. Check for extraneous solutions. \((2 x+3)^{\frac{1}{2}}-7=0\)

Find the inverse of each function. Is the inverse a function? $$ f(x)=\sqrt{2 x-1}+3 $$