AN44 Answers: Chapter 5 36. 16 9 { } − 37. 1 3 2 , 1 3 2 { } − − − + 38. 1 4{ } 39. 2 ln 3 ln 5 ln 3 { } − 40. 2, 6 { } − 41. 83 { } 42. 1 2 , 3 { } − 43. 1{ } 44. 1 { } − 45. 1 ln 5 { } − 46. ( ) { } ( ) − + = ⎧ − + ⎨ ⎪⎪ ⎩⎪⎪ ⎫ ⎬ ⎪⎪ ⎭⎪⎪ log 2 7 ln 2 7 ln3 3 47. (a), (e) y 14 x 10 y 5 x f 21(x) 5 2x21 1 2 f(x) 5 log2 (x 2 2) 1 1 0, 5 2 , 0 5 2 (3, 6) (6, 3) (b) 3; 6, 3 ( ) (c) 10; 10, 4 ( ) (d) { } > x x 5 2 or 5 2 , ( )∞ (e) f x 2 2 x 1 1 ( ) = + − − 48. (a) 37.3 W (b) 6.9 dB 49. (a) 11.77 (b) 9.56 in. 50. (a) 9.85 yr (b) 4.27 yr 51. $20,398.87; 4.04%; 17.5 yr 52. $41,668.97 53. 24,765 yr ago 54. 55.22 min, or 55 min, 13 sec 55. 8,148,316,539 56. 7.204 g; 0.519 g 57. (a) 0.3 (b) 0.8 (c) 1 0 0 25 (d) In 2026 58. (a) 1 21 0 7 (b) y 0.0903 1.3384 x ( ) = (c) N t e 0.0903 t 0.2915 ( ) = (d) 21 0 1 − 7 (e) 0.69 (f) After about 7.26 hr 59. (a) 10 210 40 0 (b) y x 18.921 7.096 ln = − (c) 10 210 40 0 (d) Approximately 3F − ° 60. (a) 50 21 0 9 (b) C e 46.9292 1 21.2733 t 0.7306 = + − (c) 21 50 0 9 (d) About 47 people; 50 people (e) 2.4 days; during the tenth hour of day 3 (f ) 9.5 days Chapter Test (page 379) 1. (a) f g x x 2 7 2 ; = + + domain: { } ≠ − x x 3 2 (b) g f 2 5 ( )( ) − = (c) f g 2 3 ( )( ) − = − 2. (a) The function is not one-to-one. (b) The function is one-to-one. 3. f x x x 2 5 3 1( ) = + − ; { } { } { } { } = ≠ = ≠ = ≠ = ≠ − − f x x f y y f x x f y y domain of 5 3 , range of 0 ; domainof 0 ; rangeof 5 3 1 1 4. The point 5, 3 ( ) − must be on the graph of f .1− 5. x 5 = 6. b 4 = 7. x 625 = 8. 2− 9. 4 10. 125 11. 7 12. (a) Domain of f : x x { } −∞< <∞ or , ( ) −∞ ∞ (b) y 16 x 2.5 (0, 2) (21, 21) y 5 22 (c) Range of f : y y 2 { } >− or 2, ( ) − ∞ Horizontal asymptote: y 2 = − (d) f x x log 2 1 1 4 ( ) ( ) = + − − (e) Domain of f x x : 2 1 { } >− − or 2, ( ) − ∞ Range of f y y : 1 { } −∞< <∞ − or , ( ) −∞∞ (f ) x 5 22 y 5 x 5 (2, 0) (21, 21) 13. (a) Domain of f : x x 2 { } > or 2, ( )∞ (b) x 5 2 y 8 x 18 (7, 0) (3, 1) (c) Range of f : y y { } −∞< <∞ or , ( ) −∞ ∞ Vertical asymptote: x 2 = (d) f x 5 2 x 1 1 ( ) = + − − (e) Domain of f x x : 1 { } −∞< <∞ − or , ( ) −∞ ∞ f y y Range of : 2 or 2, 1 { } ( ) > ∞ − (f ) y 8 x 8 (0, 7) (1, 3) y 5 2 14. 1{ } 15. 91 { } 16. ln 2 { } − 17. 1 13 2 , 1 13 2 { } − + 18. 3 ln 7 1 ln 7 { } − 19. 2 6 { } 20. x x x 2 3 log log 6 log 3 2 2 2 ( ) ( ) + − − − + 21. About 250.39 days 22. (a) $1033.82 (b) $963.42 (c) 11.9 yr 23. (a) About 83 dB (b) The pain threshold will be exceeded if 31,623 people shout at the same time.
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