Chapter 7

Solve each equation. $$ \sqrt{4 x+1}=3 $$

Write each expression in radical form. $$ 7^{\frac{1}{3}} $$

Simplify. 5\(\sqrt{63}\)

Simplify. $$ \sqrt[3]{64} $$

Graph each function. State the domain and range of the function. \(y=\sqrt{x}+2\)

Find the inverse of each relation. $$ \\{(2,4),(-3,1),(2,8)\\} $$

Find \((f+g)(x),(f-g)(x),(f \cdot g)(x),\) and \(\left(\frac{f}{g}\right)\) for each \(f(x)\) and \(g(x)\) $$ \begin{array}{l}{f(x)=3 x+4} \\ {g(x)=5+x}\end{array} $$

Solve each equation. $$ 4-(7-y)^{\frac{1}{2}}=0 $$

Write each expression in radical form. $$ x^{\frac{2}{3}} $$

Simplify. \(\sqrt[4]{16 x^{5} y^{4}}\)

Simplify. $$ \sqrt{(-2)^{2}} $$

Graph each function. State the domain and range of the function. \(y=\sqrt{4 x}\)

Find the inverse of each relation. $$ \\{(1,3),(1,-1),(1,-3),(1,1)\\} $$

Find \((f+g)(x),(f-g)(x),(f \cdot g)(x),\) and \(\left(\frac{f}{g}\right)\) for each \(f(x)\) and \(g(x)\) $$ \begin{array}{l}{f(x)=x^{2}+3} \\ {g(x)=x-4}\end{array} $$

Solve each equation. $$ 1+\sqrt{x+2}=0 $$

Write each radical using rational exponents. $$ \sqrt[4]{26} $$

Simplify. \(\sqrt{75 x^{3} y^{6}}\)

Simplify. $$ \sqrt[5]{-243} $$

Graph each function. State the domain and range of the function. \(y=\sqrt{x-1}+3\)

Find the inverse of each function. Then graph the function and its inverse. $$ f(x)=-x $$

For each pair of functions, find \(f \circ g\) and \(g \circ f,\) if they exist. $$ \begin{array}{l}{f=\\{(-1,9),(4,7)\\}} \\\ {g=\\{(-5,4),(7,12),(4,-1)\\}}\end{array} $$

Write each radical using rational exponents. $$ \sqrt[3]{6 x^{5} y^{7}} $$

Simplify. \(\sqrt{\frac{7}{8 y}}\)

When fighting a fire, the velocity \(v\) of water being pumped into the air is the square root of twice the product of the maximum height \(h\) and \(g\) , the acceleration due to gravity \(\left(32 \mathrm{ft} / \mathrm{s}^{2}\right) .\) Determine an equation that will give the maximum height of the water as a function of its velocity.

Find the inverse of each function. Then graph the function and its inverse. $$ g(x)=3 x+1 $$

Solve each equation. $$ \frac{1}{6}(12 a)^{\frac{1}{3}}=1 $$

Evaluate each expression. $$ 125^{\frac{1}{3}} $$

Simplify. \(\sqrt{\frac{a^{7}}{b^{9}}}\)

Simplify. $$ \sqrt[3]{x^{3}} $$

The Coolville Fire Department must purchase a pump that will propel water 80 feet into the air. Will a pump that is advertised to project water with a velocity of 75 ft/s meet the fire department’s need? Explain.

Find the inverse of each function. Then graph the function and its inverse. $$ y=\frac{1}{2} x+5 $$

Find \([g \circ h](x)\) and \([h \circ g](x)\) $$ \begin{array}{l}{g(x)=2 x} \\ {h(x)=3 x-4}\end{array} $$

Solve each equation. $$ \sqrt[3]{x-4}=3 $$

Evaluate each expression. $$ 81^{-\frac{1}{4}} $$

Simplify. \(\sqrt[3]{\frac{2}{3 x}}\)

Simplify. $$ \sqrt[4]{y^{4}} $$

Graph each inequality. \(y \leq \sqrt{x-4}+1\)

Find \([g \circ h](x)\) and \([h \circ g](x)\) $$ \begin{array}{l}{g(x)=x+5} \\ {h(x)=x^{2}+6}\end{array} $$

Solve each equation. $$ (3 y)^{\frac{1}{3}}+2=5 $$

Evaluate each expression. $$ 27^{\frac{2}{3}} $$

Under certain conditions, a police accident investigator can use the formula \(s=\frac{10 \sqrt{\ell}}{\sqrt{5}}\) to estimate the speed \(s\) of a car in miles per hour based on the length \(\ell\) in feet of the skid marks it left. Write the formula without a radical in the denominator.

Simplify. $$ \sqrt{36 a^{2} b^{4}} $$

Graph each inequality. \(y>\sqrt{2 x+4}\)

For Exercises 6 and \(7,\) use the following information. The acceleration due to gravity is 9.8 meters per second squared \(\left(\mathrm{m} / \mathrm{s}^{2}\right) .\) To convert to feet per second squared, you can use the following operations. An object is accelerating at 50 feet per second squared. How fast is it accelerating in meters per second squared?

If \(f(x)=3 x, g(x)=x+7,\) and \(h(x)=x^{2},\) find each value. $$ f[g(3)] $$

Solve each inequality. $$ \sqrt{2 x+3}-4 \leq 5 $$

Evaluate each expression. $$ \frac{54}{9^{\frac{3}{2}}} $$

Under certain conditions, a police accident investigator can use the formula \(s=\frac{10 \sqrt{\ell}}{\sqrt{5}}\) to estimate the speed \(s\) of a car in miles per hour based on the length \(\ell\) in feet of the skid marks it left. How fast was a car traveling that left skid marks 120 feet long?

Simplify. $$ \sqrt{(4 x+3 y)^{2}} $$

Graph each inequality. \(y \geq \sqrt{x+2}-1\)