In Exercises 53-72, find expressions for (fo g) (x) and (gof) (x). Give the domains of fog and gof.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Last question for the night! I’m sort of understanding the compositions. But, the polynomials are confusing me. Can you please advise on questions , 67 and 68. I’m able to resolve (g o f)(x), but not f o g. I’d like to see if my answers are correct. Thank you so much!!
In Exercises 53-72, find expressions for (fo g) (x) and (gof) (x). Give the domains of fog and g•f.
53. f(x) = -x² + 1, g(x) = x + 1
54. fAx) = 2x + 5, g(x) = 3x?
%3D
x + 1
x- 3
55. f(x) = 4x - 1, g(x) =
4
56. f(x) = 2x + 3, g(x) =
",2
%3D
%3D
57. flx) = 3x² + 4x, gfx) = x + 2
58. f(x)
= -2x + 1, g(x) = 2x? – 5x
1
59. flx) = g(x) = 2x + 5
60. f(x) = 3x + 1, g(x)
%3D
61. f(x) =
= 2x?
62. f(x) = 3x² + 1, g(x) :
2x + 1'
x + 5
63. f(x) = Vx + 1, g(x) = -3x - 4
64. f(x) = 5x + 1, g(x) = Vx - 3
2x
65. flx) = |xl, g(x) =
66. f(x) = |xl, g(x) =
x-3
x-1
67. f(x) = x² – 2x + 1, g(x) = x + 1
68. f(x) = x - 2, g(x) = 2x² – x + 3
%3D
r2 + 3
Transcribed Image Text:In Exercises 53-72, find expressions for (fo g) (x) and (gof) (x). Give the domains of fog and g•f. 53. f(x) = -x² + 1, g(x) = x + 1 54. fAx) = 2x + 5, g(x) = 3x? %3D x + 1 x- 3 55. f(x) = 4x - 1, g(x) = 4 56. f(x) = 2x + 3, g(x) = ",2 %3D %3D 57. flx) = 3x² + 4x, gfx) = x + 2 58. f(x) = -2x + 1, g(x) = 2x? – 5x 1 59. flx) = g(x) = 2x + 5 60. f(x) = 3x + 1, g(x) %3D 61. f(x) = = 2x? 62. f(x) = 3x² + 1, g(x) : 2x + 1' x + 5 63. f(x) = Vx + 1, g(x) = -3x - 4 64. f(x) = 5x + 1, g(x) = Vx - 3 2x 65. flx) = |xl, g(x) = 66. f(x) = |xl, g(x) = x-3 x-1 67. f(x) = x² – 2x + 1, g(x) = x + 1 68. f(x) = x - 2, g(x) = 2x² – x + 3 %3D r2 + 3
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