Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Chapter Fundamentals 1.1 Sets of Real Numbers 11 a integer, rational number a rational number a natural number, integer, rational number a rational number a rational number a irrational number irrational number irrational number Since 11 2.75 , sketch the graph: b b b b b b 10 12 rational number irrational number rational number rational number rational number irrational number natural number, integer, rational number rational number Since 87 0.875 , sketch the graph: 13 Since | 2.4 , sketch the graph: 14 Since | 0.4 , sketch the graph: 15 Since | 0.4 , sketch the graph: 16 Since | 2.4 , sketch the graph: 17 Since | 3.1 , sketch the graph: 18 Since 19 Since 20 Since 2.4 | | 1.2 , sketch the graph: 2 | 0.3 , sketch the graph: 3.4 | 2 2.2 , sketch the graph: INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Chapter Fundamentals 21 Sketching the graph: 22 Sketching the graph: 23 Sketching the graph: 24 Sketching the graph: 25 Sketching the graph: 26 Sketching the graph: 27 Sketching the graph: 28 Since 29 Since | 30 Sketching the graph: 31 False 32 False 33 True (since –2 = –2, it is also true that ––2) 34 True since 35 False 36 True since 0.777 ! 0.7000 37 False (since S | 6.2 ) 38 S +1 Đ True ă since ! â 2 39 40 41 True (since 2 | 2.8 ) True (since S | 9.61 , using the approximation S | 3.1 ) The inequality notation is x : 42 The inequality notation is 2 x : 43 The inequality notation is d x d : 44 The inequality notation is 23 d x d 45 The inequality notation is d x : 46 The inequality notation is 4 x d : 47 The inequality notation is 3 x f : 48 The inequality notation is 49 The inequality notation is 1 d x f 50 The inequality notation is d x f : 51 The inequality notation is f x : 52 The inequality notation is f x 2 : 53 The inequality notation is f x d S : S , sketch the following graph: 1.5 , sketch the graph: !2 · 2¸ ¹ : x f: INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen 54 The inequality notation is f x S Note that this is the entire number line: 55 a Since b Since c Since d Since 56 57 58 59 a 43 | 3.16 , it agrees with S to one decimal place 22 | 3.142 , it agrees with S to two decimal places 355 | 3.1415929 , it agrees with S to six decimal places 113 63 § 17 15 · | 3.1415926538 , it agrees with S to nine decimal places 25 ăâ 15 áạ We need to find two irrational numbers a and b such that their sum is rational If we choose a b , then a b , which is rational and b We need to find two irrational numbers a and b such that their sum is irrational If we choose a and b , then a b , which is irrational a We need to find two irrational numbers a and b such that their product is rational If we choose a and b , then ab 2• 16 , which is rational b We need to find two irrational numbers a and b such that their product is irrational If we choose a and b , then ab 2• , which is irrational a We need to find two irrational numbers a and b such that their quotient is rational If we choose a 12 and a 12 , which is rational b , then b and b We need to find two irrational numbers a and b such that their quotient is irrational If we choose a a , which is irrational b , then b a Raising to the 1/2 power results in 21/2 , which is irrational b Raising 60 Exercise Set 1.2 a If A 2 to the power results in 2 , which is rational is rational, then it is an example of an irrational number raised to an irrational power, resulting in a rational number b If A 2 is irrational, apply the hint to obtain: A ª ô 2 ằ ẳ Since the result is rational, we have an example of an irrational number 2 22 12 3 (1)2 (1)2 22 527 49 49 (27) 125 (4) 22 25 4 2 275 (5)2 3(4) (2)2 18 ab 56 56 49 (7)2 (3)3 bc Simplify the expression: 34 x4 34 3 43 44 >(x 1)@ 4(x 3) Since x ! : x 3 (x 3) >(x 4)@ x x (x 3) (x ) 2 x 2x (x 3) >(x 4)@ x x 1 x x 12 3x 11 Since x < –3, x + < and x + < 0, and thus: x x (x 1) >(x 3)@ x x 12 39 The absolute value equality can be written as x 40 The absolute value inequality can be written as x 41 The absolute value inequality can be written as x t 5 x 13 INSTRUCTOR OR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Exercise Set 1.2 42 The absolute value inequality can be written as x ! 43 The absolute value inequality can be written as y (4) 1, or y 44 The absolute value inequality can be written as x (1) d 0.001, or x d 0.001 45 The absolute value inequality can be written as y 3, or y 46 The absolute value inequality can be written as y t 47 The absolute value inequality can be written as x a M 48 The absolute value inequality can be written as a b t a b , or a b t a b 49 Graphing the interval x : 50 Graphing the interval x : 51 Graphing the interval x ! : 52 Graphing the interval x ! , noting that x 53 Graphing the interval x : 54 Graphing the interval x : 55 Graphing the interval x d : 56 Graphing the interval x d 57 Graphing the interval x : 58 Graphing the interval x 59 Graphing the interval x t : 60 Graphing the interval x t : 61 a 2 S 2 : !1: Graphing the interval x : b Graphing the interval x , noting that x = is excluded: 62 c The interval in part b does not include Since a = (a – b) + b, a (a b) b d a b b Subtracting b from each side, a b d a b 63 Using the triangle inequality twice: a b c 64 Since the absolute value is always non-negative, x x t Thus x x 65 solutions Consider three cases: a = b, a > b, and a < b a (b c) d a b c d a b c case 1: If a = b, then max (a, b) = a, now verifying: 12 cannot have any real ab ab aa aa 2 2a a Thus the equation is verified INSTRUCTOR USE SE ONLY ON NL (a, b) b) = a, a, and since a – b > 0, we have: have: b, then max (a, case 2: If a > b, ab ab abab 22aa a © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Chapter Fundamentals Thus the equation is verified case 3: If a < b, then max (a, b) = b, and since a – b < 0, we have: ab ab a b (a b) a b a b 2b 66 2 Thus the equation is verified Consider three cases: a = b, a > b, and a < b: case 1: If a = b, then min(a, b) = a, now verifying: b ab ab aa aa 2 2a a Thus the equation is verified case 2: If a > b, then min(a, b) = b, and since a – b > 0: ab ab Thus the equation is verified case 3: If a < b, then min(a, b) = a, and since a – b < 0: ab ab a b >(a b)@ a b a b 2a a 2 2 Thus the equation is verified 67 a Property 1(b) b c a b (a b) abab 2b b abd a b Since (a) (b) d a b , (a b) d a b d Since a b d a b and (a b) d a b , a b d a b , since a b is either a + b or –(a + b) 1.3 Solving Equations (Review and Preview) Substituting x 2 into the equation: x 4(2) 8 13 So x 2 is a solution to the equation Substituting x into each side of the equation: 1 23 12 x x So x is a solution to the equation Substituting y 3 into each side of the equation: 3 12 12 2 y y 3 3 y y (3) (3) So y 3 is not a solution to the equation Substituting y into the equation: (y 1)(y 5) So y is not a solution to the equation Substituting m So m 4 into the equation: m m 16 (5 1)(5 5) (4 )(10) 41 41 165 16 93 12 40 16 16 16 is a solution to the equation Substitute for x in the equation: 1 1 Now substitute for x in the equation: 1 Both values are solutions to the equation Solving for x: 2x 2x x 5 2 11 1 Solving for m: 2m 3m 6m 5m 6m m 12 m 122 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Precalculus-7th-Edition-by-Cohen Solving for m: 10 (2m 5) 2m m 11 13 15 Solving for t: 12 t ^4 [t (4 t )]` t ^4 [t t ]` t [4 (4)] t8 t 14 Multiplying by and then solving for x: y 1 Đ yà 3(1) ă 3(6) â 3ạ y 18 y 15 y 15 Solving for x: (x 2)(x 1) x 11 x 3x x 11 3x 11 3x x Multiplying by 15 and then solving for x: x 2x 11 5 § x· § 2x à 15 ă 15 ă 15 11 â 3ạ â x x 33 11x 33 x 3 Multiplying by and then solving for x: 14 x 1 2x 1 § x x 3à 4ă 4(0) â 1 ¹ x 4(2 x 3) x x 12 7 x 13 x 13 Multiplying by x and then solving for x: 1 x x 4x x Check: Replacing x by in the original equation yields: 3 16 3m 3m Exercise Set 1.3 4 1 33 , which is true Multiplying by 2y and then solving for y: 1 y y 2y 2y 1 2y y 23 Check: Replacing y by 2 1 3 1 5, 3 in the original equation yields: ... https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen. .. https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen. .. https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen Solution Manual for Precalculus 7th Edition by Cohen NOT FOR SALE Full file at https://TestbankDirect.eu /Solution- Manual- for- Precalculus- 7th- Edition- by- Cohen