Number 41 please. Instructions are in second photo as a function etCHAPTER 1EXERCISESN 1.4]ISE• SKIactions f and g, find f + g, f - g, f•g, and , and state the domain of each.15. f(x)In Exercises3 f(x) = 2x? – x4. f(x) = 3x + 2|2. (x)g(x) = 2x - 4= 3x + 2g(x) = x%3D1. f(x) = 2r +g(x) = 1- x2r + 3g(x) = x² – 4g(x) = x² – 25%3D10. f(x) = Vĩ%3D8. f(x) = Vx – 19. f(x) = V4- x7. f(x) = V%3D416. f(x) =g(x) = 2x?g(x) = Vx + 3g(x)ォ-43x + 2g(x) = 2Vx8(x) 3=arcises 1-20, for the given functions f and g, find the composite functionsƒ°g and g •f, and state their dom:ple 1.4.7112. f(x) = x² – 113. f(x)14. f(x)15. f(x) = |X - 1X - 3%3D11. f(x) = 2x + 1g(x) = 2 – xg(x) = x + 2g(x) = 2 + xg(x) =g(x) = x - 317. f(x) = Vx – 118. f(x) = V2 – x20. f(x) =16. flx) = |x - 1|119. f(x) = x³ + 4%3D13.158(x) =g(x) = x + 58(x) = x² + 2g(x) = (x – 4)\3g(x)|%3|In Exercises 21–38, evaluate the functions for the specified values, if possible.f(x) = x² + 10g(x) = Vx – 1(21.)(f+g)(2)22. (f + g)(10)23.)(f – g)(2)24. (f – g)(5)25. (f g)(4)26.(\(2)28.29. f(g(2))30. f(g(1))31. g(f(-3))32.2735. 834. \8(f(0))(((V)37. (f ° g)(4)38.In Exercises 39-50, evaluate f(g(1)) and g(f(2)), if possible.39. flx)18(x) = 2x + 1140. f(x) = x² + 1ol r41, f(x) = VT–x,%3D2- x42. f(x) = V343. f(x)|x - 1|8(x) = x + 344. f(x)g(xx'1|45. f(x) = Vx – 1,1g(x) = x² + 5 46. f(x) = Vx - 3, g(x)%3D|1%3D|47. f(x)%3D48. f(x) = , 8(x) = 4 – x²2- xX - 3x² - 3"%3D49. f(x) = (x - 1)3, g(x) = x² + 2x + 1|50. f(x) = (1 – x%3DIn Exercises 51-60, show that f(g(x)) = x and g(f(x)) = x.51, f(x) = 2x + 1,X - 1g(x) =2x - 252. f(x) = , g(x) = 3x + 2353. f(x) = Vx - 1, g(x) = x2 + 1 for x 1%3D54, f(x) = 2- x², g(x) = V2 – x fog(x) = V2 - x fo|5. fx)=%3D1= g(x) = - for x # 056. f(x) = (5 – x)/³, g(x) = 5 – x³%3D%3Dflx) = 4x - 9,Vx + 9%3Dg(x) :for x 2058. f(x) = V&x – 1, g(x)%3D+1Hx) = glx) =1x+ 1for x # 0, x # 18.60.f(x).V25 - r?25 31. g(f(-3))32. g(f(4))37. (f o g)(4)38. (g º f)(-3)41, f(x) = VI – x, g(x) = x² + 2%3D|1.

Name: Number 41 please. Instructions are in second photo as a function etCHA
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Description: Number 41 please. Instructions are in second photo as a function etCHAPTER 1EXERCISESN 1.4]ISE• SKIactions f and g, find f + g, f - g, f•g, and , and state the domain of each.15. f(x)In Exercises3 f(x) = 2x? – x4. f(x) = 3x + 2|2. (x)g(x) = 2x - 4= 3

We have to find the value of composition function

Answered: 31. g(f(-3)) 32. g(f(4)) 37. (f o g)(4)…

Math

Calculus

31. g(f(-3)) 32. g(f(4)) 37. (f o g)(4) 38. (g º f)(-3) 41, f(x) = VI – x, g(x) = x² + 2 %3D | 1.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

Number 41 please. Instructions are in second photo

as a function et
CHAPTER 1
EXERCISES
N 1.4]
ISE
• SKI
actions f and g, find f + g, f - g, f•g, and , and state the domain of each.
1
5. f(x)
In Exercises
3 f(x) = 2x? – x
4. f(x) = 3x + 2
|
2. (x)
g(x) = 2x - 4
= 3x + 2
g(x) = x
%3D
1. f(x) = 2r +
g(x) = 1- x
2r + 3
g(x) = x² – 4
g(x) = x² – 25
%3D
10. f(x) = Vĩ
%3D
8. f(x) = Vx – 1
9. f(x) = V4- x
7. f(x) = V
%3D
4
1
6. f(x) =
g(x) = 2x?
g(x) = Vx + 3
g(x)
ォ-4
3x + 2
g(x) = 2Vx
8(x) 3=
arcises 1-20, for the given functions f and g, find the composite functionsƒ°g and g •f, and state their dom:
ple 1.4.7
1
12. f(x) = x² – 1
13. f(x)
14. f(x)
15. f(x) = |
X - 1
X - 3
%3D
11. f(x) = 2x + 1
g(x) = 2 – x
g(x) = x + 2
g(x) = 2 + x
g(x) =
g(x) = x - 3
17. f(x) = Vx – 1
18. f(x) = V2 – x
20. f(x) =
16. flx) = |x - 1|
1
19. f(x) = x³ + 4
%3D
13.15
8(x) =
g(x) = x + 5
8(x) = x² + 2
g(x) = (x – 4)\3
g(x)
|
%3|
In Exercises 21–38, evaluate the functions for the specified values, if possible.
f(x) = x² + 10
g(x) = Vx – 1
(
21.)(f+g)(2)
22. (f + g)(10)
23.)(f – g)(2)
24. (f – g)(5)
25. (f g)(4)
26.
(\(2)
28.
29. f(g(2))
30. f(g(1))
31. g(f(-3))
32.
27
35. 8
34. \8(f(0))
(((V)
37. (f ° g)(4)
38.
In Exercises 39-50, evaluate f(g(1)) and g(f(2)), if possible.
39. flx)
1
8(x) = 2x + 1
1
40. f(x) = x² + 1
ol r
41, f(x) = VT–x,
%3D
2- x
42. f(x) = V3
43. f(x)
|x - 1|
8(x) = x + 3
44. f(x)
g(x
x'
1
|
45. f(x) = Vx – 1,
1
g(x) = x² + 5 46. f(x) = Vx - 3, g(x)
%3D
|
1
%3D
|
47. f(x)
%3D
48. f(x) = , 8(x) = 4 – x²
2- x
X - 3
x² - 3"
%3D
49. f(x) = (x - 1)3, g(x) = x² + 2x + 1
|
50. f(x) = (1 – x
%3D
In Exercises 51-60, show that f(g(x)) = x and g(f(x)) = x.
51, f(x) = 2x + 1,
X - 1
g(x) =
2
x - 2
52. f(x) = , g(x) = 3x + 2
3
53. f(x) = Vx - 1, g(x) = x2 + 1 for x 1
%3D
54, f(x) = 2- x², g(x) = V2 – x fo
g(x) = V2 - x fo
|
5. fx)=
%3D
1
= g(x) = - for x # 0
56. f(x) = (5 – x)/³, g(x) = 5 – x³
%3D
%3D
flx) = 4x - 9,
Vx + 9
%3D
g(x) :
for x 20
58. f(x) = V&x – 1, g(x)
%3D
+1
Hx) = glx) =
1
x+ 1
for x # 0, x # 1
8.
60.
f(x).
V25 - r?
25

31. g(f(-3))
32. g(f(4))
37. (f o g)(4)
38. (g º f)(-3)
41, f(x) = VI – x, g(x) = x² + 2
%3D
|
1.

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