5_2 - Chapter 5 Exponential and Logarithmic Functions 5.2...

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Chapter 5 638 Exponential and Logarithmic Functions 5.2 Inverse Functions 1. The set of ordered pairs is a function because there are no ordered pairs with the same first element and different second elements. 2. Increasing on the interval 0, ( 29 . Decreasing on the interval -∞ ,0 ( 29 . 3. Increasing on the interval -∞ , ( 29 . 4. one-to-one 5. y = x 6. 4, [ 29 7. False 8. True 9. (a) Domain $200 $300 $350 $425 Range 20 hours 25 hours 30 hours 40 hours (b) Inverse is a function since each element in the domain corresponds to one and only one element in the range. 10. (a) Domain Beth Diane Linda Marcia Range Bob Dave John Chuck (b) Inverse is a function since each element in the domain corresponds to one and only one element in the range. 11. (a) Domain $200 $350 $425 Range 20 hours 25 hours 30 hours 40 hours (b) Inverse is not a function since domain element $200 corresponds to two different elements in the range. 12. (a) Domain Beth Diane Marcia Range Bob Dave John Chuck (b) Inverse is not a function since domain element Marcia corresponds to two different elements in the range.
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Section 5.2 Inverse Functions 639 13. (a) (6,2),(6, - 3), (9, 4), (10,1) { } (b) Inverse is not a function since domain element 6 corresponds to two different elements in the range. 14. (a) (5, – 2), (3, - 1), (7, 3), (12, 4) { } (b) Inverse is a function since each element in the domain corresponds to one and only one element in the range. 15. (a) (0,0),(1,1), (16,2), (81,3) { } (b) Inverse is a function since each element in the domain corresponds to one and only one element in the range. 16. (a) (2, 1), (8, 2), (18, 3), (32, 4) { } (b) Inverse is a function since each element in the domain corresponds to one and only one element in the range. 17. Every horizontal line intersects the graph of f at exactly one point. One-to-one. 18. Every horizontal line intersects the graph of f at exactly one point. One-to-one. 19. There are horizontal lines that intersect the graph of f at more than one point. Not one-to-one. 20. There are horizontal lines that intersect the graph of f at more than one point. Not one-to-one. 21. Every horizontal line intersects the graph of f at exactly one point. One-to-one. 22. The horizontal line y = 2 intersects the graph of f at every point. Not one-to-one. 23. Graphing the inverse: 24. Graphing the inverse:
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Chapter 5 Exponential and Logarithmic Functions 640 25. Graphing the inverse: 26. Graphing the inverse: 27. Graphing the inverse: 28. Graphing the inverse: 29. f ( x ) = 3 x + 4, g ( x ) = 1 3 ( x - 4) f ( g ( x )) = f 1 3 ( x - 4) = 3 1 3 ( x - 4)  + 4 = ( x - 4) + 4 = x g ( f ( x )) = g (3 x + 4) = 1 3 (3 x + 4) - 4 ( 29 = 1 3 (3 x ) = x 30. f
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This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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5_2 - Chapter 5 Exponential and Logarithmic Functions 5.2...

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