446 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions For each function that is one-to-one, (a) write an equation for the inverse function, (b) graph ƒ and ƒ-1 on the same axes, and (c) give the domain and range of both f and ƒ-1. If the function is not one-to-one, say so. See Examples 5–8. 59. ƒ1x2 = 3x - 4 60. ƒ1x2 = 4x - 5 61. ƒ1x2 = -4x + 3 62. ƒ1x2 = -6x - 8 63. ƒ1x2 = x3 + 1 64. ƒ1x2 = -x3 - 2 65. ƒ1x2 = x2 + 8 66. ƒ1x2 = -x2 + 2 67. ƒ1x2 = 1 x , x ≠0 68. ƒ1x2 = 4 x , x ≠0 69. ƒ1x2 = 1 x - 3 , x ≠3 70. ƒ1x2 = 1 x + 2 , x ≠-2 71. ƒ1x2 = x + 1 x - 3 , x ≠3 72. ƒ1x2 = x + 2 x - 1 , x ≠1 73. ƒ1x2 = 2x + 6 x - 3 , x ≠3 74. ƒ1x2 = -3x + 12 x - 6 , x ≠6 75. ƒ1x2 = 2x + 6, x Ú -6 76. ƒ1x2 = -2x2 - 16, x Ú 4 Graph the inverse of each one-to-one function. See Example 7. 77. 0 x y 78. 0 x y 79. 0 x y 80. 0 x y 81. 0 x y 82. 0 x y Concept Check The graph of a function ƒ is shown in the figure. Use the graph to find each value. 83. ƒ-1142 84. ƒ-1122 85. ƒ-1102 86. ƒ-11-22 87. ƒ-11-32 88. ƒ-11-42 Concept Check Answer each of the following. 89. Suppose ƒ1x2 is the number of cars that can be built for x dollars. What does ƒ-1110002 represent? 90. Suppose ƒ1r2 is the volume (in cubic inches) of a sphere of radius r inches. What does ƒ-1152 represent? 91. Show that any function of the form ƒ1x2 = -x + b is its own inverse. 92. For a one-to-one function ƒ, find 1ƒ-1 ∘ ƒ2122, where ƒ122 = 3. –2 2 –2 –4 4 2 –4 4 0 x y
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