Chapter 1

Solve each equation. $$x^{3 / 2}=125$$

Solve each equation or inequality. $$|4 x+3|>0$$

Find each product. Write the answer in standard form. $$-5 i(4-3 i)^{2}$$

Celsius and Fahrenheit Temperatures In the met- ric system of weights and measures, temperature is measured in degrees Celsius (" \(^{\circ}\) C) instead of degrees Fahrenheit \(\left(^{\circ} \mathrm{F}\right) .\) To convert between the two systems, we use the equations $$ C=\frac{5}{9}(F-32) \quad \text { and } \quad F=\frac{9}{5} C+32 $$ In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. $$350^{\circ} \mathrm{F}$$

Solve each equation. $$x^{5 / 4}=32$$

Explain why the following equations have the same solution set. (Do not actually solve. \()\) $$ -2 x^{2}+3 x-6=0 \quad \text { and } \quad 2 x^{2}-3 x+6=0 $$

For \(x^{2}-x\) to have an absolute value equal to \(6,\) what are the two possible values that it may be? (Hint: One is positive and the other is negative.)

Find each product. Write the answer in standard form. $$(2+i)(2-i)(4+3 i)$$

Temperature of Venus Venus is the hottest planet with a surface temperature of \(867^{\circ} \mathrm{F}\). What is this temperature in Celsius? (Source: World Almanac and Book of Facts.)

Solve each equation. $$\left(x^{2}+24 x\right)^{1 / 4}=3$$

Solve each cubic equation using factoring and the quadratic formula. $$x^{3}-8=0$$

Find each product. Write the answer in standard form. $$(3-i)(3+i)(2-6 i)$$

Solve each equation. $$\left(3 x^{2}+52 x\right)^{1 / 4}=4$$

Solve each cubic equation using factoring and the quadratic formula. $$x^{3}-27=0$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{6+2 i}{1+2 i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{x-3}{x+5} \leq 0$$

Temperature in Montreal The average low temperature in Montreal, Canada, for the date January 30 is \(7^{\circ} \mathrm{F}\). What is the corresponding Celsius temperature to the nearest tenth of a degree? (Source: www.wunderground.com)

Solve each equation. $$(x-3)^{2 / 5}=4$$

Solve each cubic equation using factoring and the quadratic formula. $$x^{3}+27=0$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$ \frac{14+5 i}{3+2 i} $$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{x+1}{x-4}>0$$

Temperature in Haiti The average annual temperature in Port-au-Prince, Haiti, is approximately \(28.1^{\circ} \mathrm{C} .\) What is the corresponding Fahrenheit temperature to the nearest tenth of a degree? (Source: www.climatetemp.info/haiti)

Solve each equation. $$(x+200)^{2 / 3}=36$$

Solve each cubic equation using factoring and the quadratic formula. $$x^{3}+64=0$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{2-i}{2+i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{1-x}{x+2}<-1$$

Solve each equation. $$(2 x+5)^{1 / 3}-(6 x-1)^{1 / 3}=0$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$s=\frac{1}{2} g t^{2}, \quad \text { for } t$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = ƒ -11x2, (b) graph ƒ and ƒ -1 on the same axes, and (c) give the domain and the range of ƒ and ƒ -1. If the function is not one-to-one, say so. $$f(x)=\frac{x+1}{x-3}, \quad x \neq 3$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{6-x}{x+2}>1$$

Solve each equation. $$(3 x+7)^{1 / 3}-(4 x+2)^{1 / 3}=0$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$\mathscr{A}=\pi r^{2}, \quad \text { for } r$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = ƒ -11x2, (b) graph ƒ and ƒ -1 on the same axes, and (c) give the domain and the range of ƒ and ƒ -1. If the function is not one-to-one, say so. $$f(x)=\frac{x+2}{x-1}, \quad x \neq 1$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{1-3 i}{1+i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{3}{x-6} \leq 2$$

Solve each equation. $$(2 x-1)^{2 / 3}=x^{1 / 3}$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$F=\frac{k M v^{2}}{r}, \quad \text { for } v$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = ƒ -11x2, (b) graph ƒ and ƒ -1 on the same axes, and (c) give the domain and the range of ƒ and ƒ -1. If the function is not one-to-one, say so. $$f(x)=\frac{-3 x+12}{x-6}, \quad x \neq 6$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{-3+4 i}{2-i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{3}{x-2}<1$$

Solve each equation. $$(x-3)^{2 / 5}=(4 x)^{1 / 5}$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$E=\frac{e^{2} k}{2 r}, \quad \text { for } e$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = ƒ -11x2, (b) graph ƒ and ƒ -1 on the same axes, and (c) give the domain and the range of ƒ and ƒ -1. If the function is not one-to-one, say so. $$f(x)=\frac{-3 x+12}{x-6}, \quad x \neq 6$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{-5}{i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{-4}{1-x}<5$$

Solve each equation. $$x^{2 / 3}=2 x^{1 / 3}$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = ƒ -11x2, (b) graph ƒ and ƒ -1 on the same axes, and (c) give the domain and the range of ƒ and ƒ -1. If the function is not one-to-one, say so. $$f(x)=\sqrt{6+x}, \quad x \geq-6$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{-6}{i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{-6}{3 x-5} \leq 2$$

Solve each equation. $$3 x^{3 / 4}=x^{1 / 2}$$