443 4.1 Inverse Functions SOLUTION The message BE MY FACEBOOK FRIEND would be encoded as 716407619 41016 7 46 46 34 19 55 28 16 43 13 because B corresponds to 2 and ƒ122 = 3122 + 1 = 7, E corresponds to 5 and ƒ152 = 3152 + 1 = 16, and so on. Using the inverse ƒ-11x2 = 1 3x - 1 3 to decode yields ƒ-1172 = 1 3172 - 1 3 = 2, which corresponds to B, ƒ-11162 = 1 31162 - 1 3 = 5, which corresponds to E, and so on. S Now Try Exercise 97. 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 4.1 Exercises CONCEPT PREVIEW Determine whether the function represented in each table is one-to-one. 1. The table shows the number of registered passenger cars in the United States for the years 2012–2016. Year Registered Passenger Cars (in thousands) 2012 111,290 2013 113,676 2014 113,899 2015 112,864 2016 112,961 Data from U.S. Federal Highway Administration. 2. The table gives the number of representatives currently in Congress from each of five New England states. State Number of Representatives Connecticut 5 Maine 2 Massachusetts 9 New Hampshire 2 Vermont 1 Data from www.house.gov CONCEPT PREVIEWFill in the blank(s) to correctly complete each sentence. 3. For a function to have an inverse, it must be . 4. If two functions ƒ and g are inverses, then 1ƒ∘ g21x2 = and = x. 5. The domain of ƒ is equal to the of ƒ-1, and the range of ƒ is equal to the of ƒ-1.
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