Exercise Set 2.4 Vocabulary Review 1. c 2. e 3. d 4. a 5. b Problems 1. 6x + 2 3. −2x + 8 5. 8x 2 + 14x − 15 7. 2x + 5 4x − 3 9. 3x − 5 + 5 x 11. 5 x − 3x + 5 13. 15 − 25 x 15. 5 3x 2 x − 5x 17. 4x − 7 19. 3x 2 − 10x + 8 21. −2x + 3 23. 3x 2 − 11x + 10 25. 9x 3 − 48x 2 + 85x − 50 27. x − 2 29. 1 x − 2 31. 3x 2 − 7x + 3 33. 6x 2 − 22x + 20, ℝ 35. 4x − 7 _ 3x 2 −11x + 10 , D = ( −∞, 5 3 ) ∪ ( 5 3 , 2 ) ∪ (2, ∞) 37. 9x 2 − 30x + 25, D = All real numbers 39. 8x 2 − 26x + 21, D = All real numbers 41. 15 43. 98 45. 3 2 47. 1 49. 40 51. 147 53. a. 81 b. 29 c. (x + 4) 2 d. x 2 + 4 55. a. −2 b. −1 c. 16x 2 + 4x − 2 d. 4x 2 + 12x − 1 57. a. 1 b. 1 3 c. 9 x 2 d. 3 x 2 59. ( f ∘ g)( x) = 5 ( x + 4 5 ) − 4 61. ( f ∘ g)( x) = 3 ( x 3 − 2 ) + 6 = x + 4 − 4 = x − 6 + 6 = x = x ( g ∘ f )(x) = (5x − 4) + 4 5 ( g ∘ f )(x) = 3x + 6 3 − 2 = 5x 5 = x + 2 − 2 = x = x 63. –1 65. − 4 3 67. 2 5 69. −2 71. 2 7 73. a. R(x) = 11.5x − 0.05x 2 b. C(x) = 2x + 200 c. P(x) = −0.05x 2 x x + 9.5x − 200 d. __ C (x) = 2 + 200 x 75. a. M(x) = 220 − x b. x M(24) = 196 c. 142 d. 135 e. 128 77. a. Coal: f( x) = 94.80x, Wind: g(x) = 97.00x b. c. h(x) = 3.20x 79. a. Coal: f( x) = 136.20x, Wind: g(x) = 97.00x b. c. h(x) = 39.20x 81. 12 83. 28 85. − 7 4 87. w = P − 2l 2 89. [–6, ∞) 91. 6 0 (–∞, 6) 93. 6, 2 95. ∅ Find the Mistake 1. e function ( f ( + g )(x) is the sum of the functions f (x) and g (x). 2. e function ( f g ) (x) = f (x) ___ g(x) . 3. If f (x) = 3x + 4 and g (x) = x − 3, the function ( f ( + g )(x) = (3x + 4) + (x − 3) or 4x + 1. 4. For ( f ( ∘ g )(x) the numbers in the domain of the composite function must be numbers in the domain of f Landmark Review 1. 2. 3. 4. 5. Domain = { 4, 3, 1, 7 }; Range = { 3, 2, 9 }; A function 6. Domain = { 0, 1, 3 }; Range = { 3, 4, 2 }; Not a function 7. Domain = { a, 4, b, 5 }; Range = { 0, 3, 1 }; A function 8. Domain = { 1 } ; Range = { 3, 5, 2, 0 }; Not a function 9. 5 10. 12 11. 3a − 1 12. a 2 + 9a + 20 13. 5x − 4 14. x − 6 15. 6x 2 − 7x − 5 16. 3x − 5 2x + 1 17. −3 18. 16 0 20 40 60 80 100 0 5,000 10,000 dollars Dollars mWh g(x) f(x) (100, 9,700) (100, 9,480) 0 20 40 60 80 100 0 5,000 10,000 dollars Dollars mWh g(x) f(x) (100, 13,620) (100, 9,480) 6 0 x y x y x y x y