Chapter 1

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. $$f(x)=-\sqrt{x^{2}-16}, \quad x \geq 4$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{8}{-i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{10}{3+2 x} \leq 5$$

Solve each equation. $$2 x^{4}-7 x^{2}+5=0$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{12}{-i}$$

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

Solve each equation. $$4 x^{4}-8 x^{2}+3=0$$

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

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

Solve each rational inequality. Write each solution set in interval notation. $$\frac{7}{x+2} \geq \frac{1}{x+2}$$

Solve each equation. $$x^{4}+2 x^{2}-15=0$$

For each equation, ( \(a\) ) solve for \(x\) in terms of \(y,\) and ( \(b\) ) solve for \(y\) in terms of \(x\). $$4 x^{2}-2 x y+3 y^{2}=2$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{5}{9 i}$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{5}{x+1}>\frac{12}{x+1}$$

Solve each equation. $$3 x^{4}+10 x^{2}-25=0$$

For each equation, ( \(a\) ) solve for \(x\) in terms of \(y,\) and ( \(b\) ) solve for \(y\) in terms of \(x\). $$3 y^{2}+4 x y-9 x^{2}=-1$$

Graph the inverse of each one-to-one function.

Complex numbers are used to describe current I, voltage \(E,\) and impedance \(Z\) (the opposition to current). These three quantities are related by the equation \(E=I Z, \quad\) which is known as Ohm's Law. Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the equation \(E=I Z\) for the remaining value. $$I=5+7 i, Z=6+4 i$$

Write an equation involving absolute value that says the distance between \(p\) and \(q\) is 2 units.

Solve each rational inequality. Write each solution set in interval notation. $$\frac{3}{2 x-1}>\frac{-4}{x}$$

Solve each equation. $$(x-1)^{2 / 3}+(x-1)^{1 / 3}-12=0$$

For each equation, ( \(a\) ) solve for \(x\) in terms of \(y,\) and ( \(b\) ) solve for \(y\) in terms of \(x\). $$2 x^{2}+4 x y-3 y^{2}=2$$

Complex numbers are used to describe current I, voltage \(E,\) and impedance \(Z\) (the opposition to current). These three quantities are related by the equation \(E=I Z, \quad\) which is known as Ohm's Law. Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the equation \(E=I Z\) for the remaining value. $$I=20+12 i, Z=10-5 i$$

Write an equation involving absolute value that says the distance between \(r\) and \(s\) is 6 units.

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

For each equation, ( \(a\) ) solve for \(x\) in terms of \(y,\) and ( \(b\) ) solve for \(y\) in terms of \(x\). $$5 x^{2}-6 x y+2 y^{2}=1$$

Graph the inverse of each one-to-one function.

Complex numbers are used to describe current I, voltage \(E,\) and impedance \(Z\) (the opposition to current). These three quantities are related by the equation \(E=I Z, \quad\) which is known as Ohm's Law. Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the equation \(E=I Z\) for the remaining value. $$I=10+4 i, E=88+128 i$$

Write each statement as an absolute value equation or inequality. \(m\) is no more than 2 units from 7.

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

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$x^{2}-8 x+16=0$$

Complex numbers are used to describe current I, voltage \(E,\) and impedance \(Z\) (the opposition to current). These three quantities are related by the equation \(E=I Z, \quad\) which is known as Ohm's Law. Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the equation \(E=I Z\) for the remaining value. $$E=57+67 i, Z=9+5 i$$

Write each statement as an absolute value equation or inequality. \(z\) is no less than 5 units from 4.

Solve each equation. $$(x+5)^{2 / 3}+(x+5)^{1 / 3}-20=0$$

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$x^{2}+4 x+4=0$$

Simplify each power of i. $$i^{25}$$

Write each statement as an absolute value equation or inequality. \(p\) is within 0.0001 unit of 9.

Solve each rational inequality. Write each solution set in interval notation. $$\frac{x+3}{x-5} \leq 1$$$

Solve each equation. $$6(x+2)^{4}-11(x+2)^{2}=-4$$

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$3 x^{2}+5 x+2=0$$

Simplify each power of i. $$i^{29}$$

Write each statement as an absolute value equation or inequality. \(k\) is within 0.0002 unit of \(10 .\)

Solve each rational inequality. Write each solution set in interval notation. \(4\frac{x+2}{3+2 x} \leq 5\)4

Solve each equation. $$8(x-4)^{4}-10(x-4)^{2}=-3$$

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$8 x^{2}=-14 x-3$$

Simplify each power of i. $$i^{22}$$

Write each statement as an absolute value equation or inequality. \(r\) is no less than 1 unit from 29.

Solve each rational inequality. Write each solution set in interval notation.4 $$\frac{2 x-3}{x^{2}+1} \geq 0$4

Solve each equation. $$10 x^{-2}+33 x^{-1}-7=0$$

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$4 x^{2}=-6 x+3$$