309 2.8 Function Operations and Composition 49. ƒ1x2 = 1 x 50. ƒ1x2 = 1 x2 51. ƒ1x2 = x2 52. ƒ1x2 = -x2 53. ƒ1x2 = 1 - x2 54. ƒ1x2 = 1 + 2x2 55. ƒ1x2 = x2 + 3x + 1 56. ƒ1x2 = x2 - 4x + 2 Let ƒ1x2 = 2x - 3 and g1x2 = -x + 3. Find each function value. See Example 5. 57. 1ƒ∘ g2142 58. 1ƒ∘ g2122 59. 1ƒ∘ g21-22 60. 1g∘ ƒ2132 61. 1g∘ ƒ2102 62. 1g∘ ƒ21-22 63. 1ƒ∘ ƒ2122 64. 1g∘ g21-22 Find each of the following. 65. 1ƒ∘ g2122 66. 1ƒ∘ g2172 67. 1g∘ ƒ2132 68. 1g∘ ƒ2162 69. 1ƒ∘ ƒ2142 70. 1g∘ g2112 71. Concept Check Why can we not determine 1ƒ∘ g2112 given the information in the tables for Exercises 65–70? 72. Concept Check Extend the concept of composition of functions to evaluate 1g∘ 1ƒ∘ g22172 using the tables for Exercises 65–70. Concept Check The tables give some selected ordered pairs for functions ƒ and g. x 3 4 6 ƒ1x2 1 3 9 x 2 7 1 9 g1x2 3 6 9 12 Given functions f and g, find (a) 1ƒ∘ g21x2 and its domain, and (b) 1g∘ ƒ21x2 and its domain. See Examples 6 and 7. 73. ƒ1x2 = -6x + 9, g1x2 = 5x + 7 74. ƒ1x2 = 8x + 12, g1x2 = 3x - 1 75. ƒ1x2 = 2x, g1x2 = x + 3 76. ƒ1x2 = 2x, g1x2 = x - 1 77. ƒ1x2 = x3, g1x2 = x2 + 3x - 1 78. ƒ1x2 = x + 2, g1x2 = x4 + x2 - 4 79. ƒ1x2 = 2x - 1, g1x2 = 3x 80. ƒ1x2 = 2x - 2, g1x2 = 2x 81. ƒ1x2 = 2 x , g1x2 = x + 1 82. ƒ1x2 = 4 x , g1x2 = x + 4 83. ƒ1x2 = 2x + 2, g1x2 = - 1 x 84. ƒ1x2 = 2x + 4, g1x2 = - 2 x 85. ƒ1x2 = 2x, g1x2 = 1 x + 5 86. ƒ1x2 = 2x, g1x2 = 3 x + 6 87. ƒ1x2 = 1 x - 2 , g1x2 = 1 x 88. ƒ1x2 = 1 x + 4 , g1x2 = - 1 x 89. Concept Check Fill in the missing entries in the table. x ƒ1x2 g1x2 g1ƒ1x2 2 1 3 2 7 2 1 5 3 2
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