Chapter 7

Graph each relation and its inverse. $$ y=2 x-3 $$

The maximum flow of water in a pipe is modeled by the formula \(Q=A v,\) where \(A\) is the cross-sectional area of the pipe and \(v\) is the velocity of the water. Find the diameter of a pipe that allows a maximum flow of 50 \(\mathrm{ft}^{3} / \mathrm{min}\) of water flowing at a velocity of 600 \(\mathrm{ft} / \mathrm{min}\) . Round your answer to the nearest inch.

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ g(x)-f(x) $$

Multiply. $$ (2+\sqrt{7})(1+3 \sqrt{7}) $$

Simplify. Assume that all variables are positive. $$ \sqrt{200 a^{6} b^{7}} $$

Write each expression in radical form. $$ y^{-\frac{9}{8}} $$

Find each real-number root. $$ -\sqrt{36} $$

Graph each function. \(y=-\sqrt{x-3}+2\)

Graph each relation and its inverse. $$ y=3-7 x $$

Solve. Check for extraneous solutions. \(\sqrt{11 x+3}-2 x=0\)

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ f(x)-g(x) $$

Multiply. $$ (3-4 \sqrt{2})(5-6 \sqrt{2}) $$

Write each expression in radical form. $$ t^{-\frac{3}{4}} $$

Graph each function. \(y=\frac{1}{4} \sqrt{x+2}-1\)

Graph each relation and its inverse. $$ y=-x $$

Solve. Check for extraneous solutions. \((5 x+4)^{\frac{1}{2}}-3 x=0\)

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ f(x) \cdot g(x) $$

Multiply. $$ (\sqrt{3}+\sqrt{5})^{2} $$

Simplify. Assume that all variables are positive. $$ \sqrt[4]{64 x^{3} y^{6}} $$

Write each expression in radical form. $$x^{1.5}$$

Find each real-number root. $$ \sqrt{0.36} $$

Graph each function. \(y=3 \sqrt{x+1}+4\)

Solve. Check for extraneous solutions. \(\sqrt{3 x+13}-5=x\)

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ \frac{f(x)}{g(x)} $$

Multiply. $$ (\sqrt{13}+6)^{2} $$

Multiply and simplify. Assume that all variables are positive. $$ \sqrt[3]{6} \cdot \sqrt[3]{16} $$

Write each expression in radical form. $$y^{1.2}$$

Graph each relation and its inverse. $$ y=3 x^{2} $$

Find each real-number root. $$ -\sqrt[3]{64} $$

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

Graph each relation and its inverse. $$ y=-x^{2} $$

Solve. Check for extraneous solutions. \(\sqrt{x+7}+5=x\)

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ \frac{g(x)}{f(x)} $$

Multiply. $$ (2 \sqrt{5}+3 \sqrt{2})^{2} $$

Multiply and simplify. Assume that all variables are positive. $$ \sqrt{8 y^{5}} \cdot \sqrt{40 y^{2}} $$

Write each expression in exponential form. $$\sqrt{-10}$$

Find each real-number root. $$ \sqrt[3]{-64} $$

Graph each function. \(y=\sqrt[3]{x-4}\)

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

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.

Multiply each pair of conjugates. $$ (5-\sqrt{11})(5+\sqrt{11}) $$

Multiply and simplify. Assume that all variables are positive. $$ \sqrt{7 x^{5}} \cdot \sqrt{42 x y^{9}} $$

Write each expression in exponential form. $$\sqrt{7 x^{3}}$$

Graph each relation and its inverse. $$ y=4 x^{2}-2 $$

Find each real-number root. $$ -\sqrt[4]{81} $$

Graph each function. \(y=\sqrt[3]{x+2}-7\)

Graph each relation and its inverse. $$ y=(x-1)^{2} $$

Solve. Check for extraneous solutions. \((5-x)^{\frac{1}{2}}=x+1\)

Use each diagram to find \((g \circ f)(x) .\) Then evaluate \((g \circ f)(3)\) and \((g \circ f)(-2)\) $$ f(x)=2 x $$ $$ g(x)=x+3 $$

Multiply each pair of conjugates. $$ (4-2 \sqrt{3})(4+2 \sqrt{3}) $$