Pre-Calc Homework Solutions 40

Pre-Calc Homework Solutions 40 - 40 Chapter 1 Review x 2 y...

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Unformatted text preview: 40 Chapter 1 Review x 2 y f 1(x) x 2 Verify. For x 0 (the domain of f 1) ( f f 1)(x) f ( f 1(x)) f ( x 2) [( x 2) 2]2 ( x)2 x For x 2 (the domain of f), ( f 1 f )(x) f 1( f(x)) f 1((x 2)2) (x 2)2 2 x 2 2 (x 2) 2 x (b) 50. For simplicity, we assume that x and y are linear functions of t and that the point (x, y) passes through ( 3, 2) for t 0 and (4, 1) for t 1. Then x f (t), where f (0) 3 and f (1) 4. Since slope = x f (t) Also, y Since slope y g(t) x t 4 1 ( 3) 0 7, 3 7t. 2 and g(1) 1 t. . 1. 7t 3 g(t), where g(0) y t 1 1 ( 2) 0 t 2 2 One possible parametrization is: x 3 7t, y 2 t, t 51. For simplicity, we assume that x and y are linear functions of t and that the point (x, y) starts at (2, 5) for t 0 and passes through ( 1, 0) for t 1. Then x f(t), where f (0) 2 and f (1) 1. Since slope Also, y slope x t y t 1 2 1 0 0 1 5 0 3, x 5, y f (t) g(t) 3t 5t 5 2 5 2 3t. [ 6, 12] by [ 4, 8] g(t), where g(0) 5 and g(1) 0. Since 5t. One possible parametrization is: x 2 3t, y 5 5t, t 0. 52. One possible parametrization is: x t, y t(t 4), t 2. 53. (a) y 3x x 2 3 2 3 1 55. Using a calculator, sin 1(0.6) 36.8699 . 56. Using a calculator, tan 1( 2.3) 66.5014 . 57. Since cos sin Therefore, 1 3 7 0.6435 radians or 1.1607 radians or 2 2 3x y y and 0 1 , 3 2 7 40 49 40 . 7 cos2 Interchange x and y. y f x 2 3 x sin cot csc 40 , 7 cos 3 40 7 40 3 , 7 tan (x) Verify. (f f 1 1 tan 1 sin , sec sin cos 1 cos 40 , 3 7 , 3 )(x) f(f f 2 2 2 3 1 (x)) x 58. (a) Note that sin 1( 0.2) 0.2014. In [0, 2 ), the solutions are x sin 1( 0.2) 3.3430 and x sin 1( 0.2) 2 6.0818. x 3 (2 1 1 2 3 x) x (b) Since the period of sin x is 2 , the solutions are x 3.3430 2k and x 6.0818 2k , k any integer. 59. e 0.2x 4 ln e 0.2x ln 4 0.2x ln 4 ln 4 x 5 ln 4 0.2 (f 1 f )(x) f f 2 3x 3 ( f(x)) (2 (2 3 3x) 3x) 60. (a) The given graph is reflected about the y-axis. y 3 (0, 2) (1, 0) 3 x (b) y = f(x) x (3, 0) [ 6, 6] by [ 4, 4] 54. (a) y y x (x 2)2, x x 2 y 2 2 3 Interchange x and y. ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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