A-25 Answers to Selected Exercises 69. (a) ƒ-11x2 = 1 + 3x x , x ≠0 (b) x y ƒ–1 ƒ –1 ƒ ƒ 0 (c) Domain of ƒ = range of ƒ-1 = 1-∞, 32 ´13, ∞2; Domain of ƒ-1 = range of ƒ = 1-∞, 02 ´10, ∞2 71. (a) ƒ-11x2 = 3x + 1 x - 1 , x ≠1 (b) x y ƒ–1 ƒ–1 ƒ ƒ –1 5 0 3 (c) Domain of ƒ = range of ƒ-1 = 1-∞, 32 ´13, ∞2; Domain of ƒ-1 = range of ƒ = 1-∞, 12 ´11, ∞2 73. (a) ƒ-11x2 = 3x + 6 x - 2 , x ≠2 (b) x 3 2 y ƒ–1 ƒ–1 ƒ ƒ (c) Domain of ƒ = range of ƒ-1 = 1-∞, 32 ´13, ∞2; Domain of ƒ-1 = range of ƒ = 1-∞, 22 ´12, ∞2 75. (a) ƒ-11x2 = x2 - 6, x Ú 0 (b) x y –6 –6 ƒ–1 ƒ 0 (c) Domain of ƒ = range of ƒ-1 = 3-6, ∞2; Domain of ƒ-1 = range of ƒ = 30, ∞2 77. x y ƒ–1 ƒ y = x 0 79. x y ƒ–1 ƒ y = x 0 81. x y ƒ–1 ƒ y = x 0 83. 4 85. 2 87. -2 89. It represents the cost, in dollars, of building 1000 cars. 91. ƒ-11x2 = -x + b 93. not one-to-one 95. one-to-one; ƒ-11x2 = -5 - 3x x - 1 , x ≠1 97. ƒ-11x2 = 1 3 x + 2 3 ; MIGUEL HAS ARRIVED 99. 6858 124 2743 63 511 124 1727 4095; ƒ-11x2 = 23 x + 1 4.2 Exercises 1. 16; 1 16 3. falls 5. 1 8; 1; 8 7. 5-36 9. 52540.226 11. 9 13. 1 9 15. 1 16 17. 16 19. 3 23 21. 1 8 23. 13.076 25. 10.267 27. x y 0 2 1 9 f(x) = 3x 29. y x 3 1 –1 1 f(x) = ( ) x 1 3 0 31. x y 0 3 5 1 f(x) = ( ) x 3 2 33. y x 1 2 –2 –1 0 1 10 f(x) = ( ) –x 1 10 35. x y –1 f(x) = 4–x 4 0 37. x y 0 3 8 f(x) = 2zxz 1 39. y x 2 –2 2 8 f(x) = 2x + 1 y = 1 0 1-∞, ∞2; 11, ∞2 41. y x 0 4 2 8 f(x) = 2x + 1 1-∞, ∞2; 10, ∞2 43. y x –4 f(x) = –2x + 2 0 2 1-∞, ∞2; 1-∞, 02 45. y x f(x) = 2–x 2 –4 0 4 1-∞, ∞2; 10, ∞2 47. x y 1 0 1 f(x) = 2x – 1 + 2 y = 2 1-∞, ∞2; 12, ∞2 49. x y 0 –3 3 –3 3 f(x) = 2x + 2 – 4 y = – 4 1-∞, ∞2; 1-4, ∞2 51. x y 0 3 3 y = –2 9 f(x) = ( )x – 2 1 3 1-∞, ∞2; 1-2, ∞2 53. x y 0 3 2 –2 9 f(x) = ( )x 1 + 2 3 1-∞, ∞2; 10, ∞2
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