447 4.2 Exponential Functions Use a graphing calculator to graph each function defined as follows, using the given viewing window. Use the graph to decide which functions are one-to-one. If a function is one-to-one, give the equation of its inverse. 93. ƒ1x2 = 6x3 + 11x2 - 6; 3-3, 24 by 3-10, 104 94. ƒ1x2 = x4 - 5x2; 3-3, 34 by 3-8, 84 95. ƒ1x2 = x - 5 x + 3 , x ≠-3; 3-8, 84 by 3-6, 84 96. ƒ1x2 = -x x - 4 , x ≠4; 3-1, 84 by 3-6, 64 Use the following alphabet coding assignment to work each problem. See Example 9. A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 J 10 K 11 L 12 M 13 N 14 O 15 P 16 Q 17 R 18 S 19 T 20 U 21 V 22 W 23 X 24 Y 25 Z 26 97. The function ƒ1x2 = 3x - 2 was used to encode a message as 37 25 19 61 13 34 22 1 55 1 52 52 25 64 13 10. Find the inverse function and determine the message. 98. The function ƒ1x2 = 2x - 9 was used to encode a message as 7 -7 35 1 -7 19 9 -3 1 -1 -7 41. Find the inverse function and determine the message. 99. Encode the message SEND HELP, using the one-to-one function ƒ1x2 = x3 - 1. Give the inverse function that the decoder will need when the message is received. 100. Encode the message SAILOR BEWARE, using the one-to-one function ƒ1x2 = 1x + 123. Give the inverse function that the decoder will need when the message is received. 4.2 Exponential Functions ■ Exponents and Properties ■ Exponential Functions ■ Exponential Equations ■ Compound Interest ■ The Number e and Continuous Compounding ■ Exponential Models Exponents and Properties Recall the definition of am/n: If a is a real number, m is an integer, n is a positive integer, and 2n a is a real number, then am/n =A!n a Bm . For example, 163/4 = A 24 16 B 3 = 23 = 8, 27-1/3 = 1 271/3 = 12 3 27 = 1 3 , and 64-1/2 = 1 641/2 = 12 64 = 1 8 .
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