1 7 2 6 х 4 x 12 6 g(x) 3 f(x) 9 3 1 Find each of the following. 67. (gof)(3) 66. (fog)(7) 65. (fog)(2) 70. (g g)(1) 69. (fo f)(4) O 68. (g f)(6) 71. Concept Check Why can we not determine (fog)(1) given the information in the tables for Exercises 65-70? 72. Concept Check Extend the concept of composition of functions to evaluate (g (fog))(7) using the tables for Exercises 65-70. Given functions fand g, find (a) (f g)(x) and its domain, and (b) (go f) (x) and its domain. See Examples 6 and 7. 74. f(x) 8x+12, g(x) 3x - 1 Зх — - 6x + 9, g(x) = 5x + 7 73. f(x) = 76. f(x) Vx, g(x) x - 1 75. f(x) Vx, g(x) x + 3eg d 78. f(x) x + 2, g(x) x4+x2 - 4 77. f(x) x3, g(x) = x2 + 3x - 1 = 80. f(x) Vx- 2, g(x) 2x 79. f(x) = Vx- 1, g(x) = 3x 03. 07. 4 82. f(x) 2 g(x) = x +1 g(x) x + 4O quiz 81. f(x) = 1 1 XX 84. f(x) Vx +4, g(x) 83. f(x) Vx +2, g(x) 1 1 X X thw ofgns 1 3 86. f(x)= Vx, g(x) - 85. f(x) Vx, g(x) = 11 x+ 5 1 8(x) 1 1 88. f(x) = 87. f(x) g(x) 11 x +4' 89. Concept Check Fill in the missing entries in the table. x-2' х f(x) g(x) g(f(x)) x 3 2 7 2 1 3 2 2/ 17 M3

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.