In Problems 43–54, the function f is one-to-one. Find its inverse and check your answer. State the domain and the range off and f. Graph f, f', and y = x on the same coordinate axes. 43. f(x) = 3x 44. f(x) = -4x 45. ƒ(x) = 4x + 2 46. f(x) — 1 -3х 47. f(x) = x³ - 1 48. f(x) = x³ + 1 49. f(x) = x² + 4 x 2 0 50. f(x) = x² + 9 xz0 4 51. f(x) = 4 3 52. f(x) = 53. f(x) = 54. f(x) x - 2 x + 2
In Problems 43–54, the function f is one-to-one. Find its inverse and check your answer. State the domain and the range off and f. Graph f, f', and y = x on the same coordinate axes. 43. f(x) = 3x 44. f(x) = -4x 45. ƒ(x) = 4x + 2 46. f(x) — 1 -3х 47. f(x) = x³ - 1 48. f(x) = x³ + 1 49. f(x) = x² + 4 x 2 0 50. f(x) = x² + 9 xz0 4 51. f(x) = 4 3 52. f(x) = 53. f(x) = 54. f(x) x - 2 x + 2
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
only 49, 53, 57, 65, 67 please.
Transcribed Image Text:In Problems 43–54, the function f is one-to-one. Find its inverse and check your answer. State the domain and the range of f and f.
Graph f, f, and y = x on the same coordinate axes.
43. f(x) = 3x
44. f(x) = -4x
45. f(x) = 4x + 2
46. f(x) = 1 – 3x
47. f(x) = x³ - 1
48. f(x) = x³ + 1
49. f(x) = x² + 4 x 2 0
50. f(x) = x² + 9 x>0
4
51. f(x) =
4
54. f(x) =
3
1
52. f(x) = -
53. f(x)
x - 2
x + 2
In Problems 55–66, the function f is one-to-one. Find its inverse and check your answer. State the domain of f and find its range usingf.
4
56. f(x) =
3x
57. f(x) =
x + 2
2
55. f(x)
3 + x
2- х
2x
3x + 1
2x
58. f(x) = -
59. f(x)
60. ƒ(x) =
x - 1
Зх — 1
Зх + 4
2х — 3
2х + 3
61. f(x) =
62. ƒ(x)
63. f(x) =
2х- 3
x + 4
x + 2
x² + 3
x > 0
3x2
-3x - 4
x² – 4
64. ƒ(x)
65. f(x)
x > 0
66. ƒ(x)
x - 2
2x2
Applications and Extensions
67. Use the graph of y = f(x) given in Problem 37 to evaluate
the following:
(a) f(-1) (b) f(1)
70. If g(-5) = 3 and g is one-to-one, what is g¯(3)?
71. The domain of a one-to-one function f is [5, ), and its range
is [-2, 00). State the domain and the range of f'.
72. The domain of a one-to-one function f is [0, ), and its range
is [5, 00). State the domain and the range of f-1.
(c) f*(1) (d) f¯1(2)
68. Use the graph of y = f(x) given in Problem 38 to evaluate
the following:
(a) f(2)
73. The domain of a one-to-one function g is the set of all real
numbers, and its range is [0, ). State the domain and the
range of g¯l.
(b) f(1) (c) f¯(0) (d) f(-1)
69. If f(7) = 13 and f is one-to-one, what is ƒ¯'(13)?
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