91Ó°ÊÓ

\(\left(5^{1 / 4}\right)+6\left(405^{1 / 4}\right)\)

In Exercises 35–46, determine whether the inverse of \(f\) is a function. Then find the inverse. $$ f(x)=-3 \sqrt{\frac{4 x-7}{3}} $$

\(f(x)=\sqrt[3]{x}\)

Between which two consecutive integers does \(\sqrt[4]{125}\) lie? Explain your reasoning.

\(\begin{aligned} 3 \sqrt[3]{12}+5 \sqrt[3]{12} &=(3+5) \sqrt[3]{24} \\ &=8 \sqrt[3]{24} \\ &=8 \sqrt[3]{8 \cdot 3} \\ &=8 \cdot 2 \sqrt[3]{3} \\ &=16 \sqrt[3]{3} \end{aligned}\)

\(f(x)=2 \sqrt{x}, g(x)=f(x+3)\)

In Exercises 47–52, solve the nonlinear system. Justify your answer with a graph. $$ \begin{aligned} &y^2=x-3 \\ &y=x-3 \end{aligned} $$

In Exercises 47–52, solve the nonlinear system. Justify your answer with a graph. $$ \begin{aligned} &y^2=4 x+17 \\ &y=x+5 \end{aligned} $$

\(f(x)=\frac{1}{3} \sqrt{x-1}, g(x)=-f(x)+9\)

MULTIPLE REPRESENTATIONS Which radical expressions are like radicals? (A) \(\left(5^{2 / 9}\right)^{3 / 2}\) (B) \(\frac{5^3}{(\sqrt[3]{5})^{8^{-}}}\) (C) \(\sqrt[3]{625}\) (D) \(\sqrt[3]{5145}-\sqrt[3]{875}\) (E) \(\sqrt[3]{5}+3 \sqrt[3]{5}\) (F) \(7 \sqrt[4]{80}-2 \sqrt[4]{405}\)