A-13 Answers to Selected Exercises 103. 1ƒ∘ g21x2 = 63,360x; It computes the number of inches in x miles. 105. (a) 12x2 = 13x2 (b) 6413 square units 107. (a) 1 ∘ r2 1t2 = 16pt2 (b) It defines the area of the leak in terms of the time t, in minutes. (c) 144p ft2 109. (a) N1x2 = 100 - x (b) G1x2 = 20 + 5x (c) C1x2 = 1100 - x2120 + 5x2 (d) $9600 111. (a) g1x2 = 1 2 x (b) ƒ1x2 = x + 1 (c) 1ƒ∘ g21x2 = ƒ1g1x22 = g1x2 + 1 = 1 2 x + 1 (d) 1ƒ∘ g21602 = 1 2 1602 + 1 = 31 (dollars) Chapter 2 Review Exercises 1. 185; A - 1 2 , 2B 3. 5; A -6, 11 2 B 5. 122, -62 7. 1x + 222 + 1y - 322 = 225 9. 1x + 822 + 1y - 122 = 289 11. x2 + y2 = 34 13. x2 + 1y - 322 = 13 15. 12, -32; 1 17. A - 7 2 , - 3 2B ; 316 2 19. not a function; 3-6, 64; 3-6, 64 21. not a function; 1-∞, ∞2; 1-∞, -14 ´31, ∞2 23. not a function; 30, ∞2; 1-∞, ∞2 25. function 27. not a function 29. 1-∞, ∞2 31. 1-∞, 24 33. -15 35. -6 37. x y 2x – 5y = 5 5 2 –2 0 39. x y 2x + 5y = 20 4 10 0 41. x y f(x) = x 1 1 0 43. x y x = –5 –5 0 45. x y y + 2 = 0 –2 0 47. x y 0 (0, 5) 3 (3, 3) 49. -2 51. 0 53. - 11 2 55. undefined 57. Initially, the car is at home. After traveling 30 mph for 1 hr, the car is 30 mi away from home. During the second hour, the car travels 20 mph until it is 50 mi away. During the third hour, the car travels toward home at 30 mph until it is 20 mi away. During the fourth hour, the car travels away from home at 40 mph until it is 60 mi away from home. During the last hour, the car travels 60 mi at 60 mph until it arrives home. 59. (a) y = 3.61x + 30.7; The slope 3.61 indicates that the percent of returns filed electronically rose an average of 3.61% per year during this period. (b) 59.6% 61. (a) y = -2x + 1 (b) 2x + y = 1 63. (a) y = 3x - 7 (b) 3x - y = 7 65. (a) y = -10 (b) y = -10 67. (a) not possible (b) x = -7 33. (a) 2 (b) 4 (c) 0 (d) - 1 3 35. (a) 3 (b) -5 (c) 2 (d) undefined 37. (a) 5 (b) 5 (c) 0 (d) undefined 39. x 1 ƒ +g2 1x2 1 ƒ −g2 1x2 1 ƒg2 1x2 Aƒ gB 1x2 -2 6 -6 0 0 0 5 5 0 undefined 2 5 9 -14 -3.5 4 15 5 50 2 41. Both the slope formula and the difference quotient represent the ratio of the vertical change to the horizontal change. The slope formula is stated for a line, while the difference quotient is stated for a function ƒ. 43. (a) 2 - x - h (b) -h (c) -1 45. (a) 6x + 6h + 2 (b) 6h (c) 6 47. (a) -2x - 2h + 5 (b) -2h (c) -2 49. (a) 1 x + h (b) -h x1x + h) (c) -1 x1x + h2 51. (a) x2 + 2xh + h2 (b) 2xh + h2 (c) 2x + h 53. (a) 1 - x2 - 2xh - h2 (b) -2xh - h2 (c) -2x - h 55. (a) x2 + 2xh + h2 + 3x + 3h + 1 (b) 2xh + h2 + 3h (c) 2x + h + 3 57. -5 59. 7 61. 6 63. -1 65. 1 67. 9 69. 1 71. g112 = 9, and ƒ192 cannot be determined from the table given. 73. (a) -30x - 33; 1-∞, ∞2 (b) -30x + 52; 1-∞, ∞2 75. (a) 2x + 3; 3-3, ∞2 (b) 2x + 3; 30, ∞2 77. (a) 1x2 + 3x - 123; 1-∞, ∞2 (b) x6 + 3x3 - 1; 1-∞, ∞2 79. (a) 23x - 1; C 1 3 , ∞B (b) 32x - 1; 31, ∞2 81. (a) 2 x + 1 ; 1-∞, -12 ´1-1, ∞2 (b) 2 x + 1; 1-∞, 02 ´ 0, ∞2 83. (a) 3- 1 x + 2 ; 1-∞, 02 ´C 1 2 , ∞B (b) - 1 1 x + 2 ; 1-2, ∞2 85. (a) 3 1 x + 5 ; 1-5, ∞2 (b) 1 1x + 5 ; 30, ∞2 87. (a) x 1 - 2x ; 1-∞, 02 ´A0, 1 2B ´A 1 2 , ∞B (b) x - 2; 1-∞, 22 ´12, ∞2 89. x ƒ1x2 g1x2 g1ƒ1x2 2 1 3 2 7 2 1 5 2 3 2 7 5 In Exercises 97–101, we give only one of the many possible ways. 97. g1x2 = 6x - 2, ƒ1x2 = x2 99. g1x2 = x2 - 1, ƒ1x2 = 1x 101. g1x2 = 6x, ƒ1x2 = 1x + 12
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