22
1 Chapter 7 Homework Radical Functions and Rational Exponents
1
Chapter 7 Homework
Radical Functions and Rational Exponents
2
pages 366–367 Exercises
1. 15, –15
2. 0.07, –0.07
3. none
4. , –
5. –4
6. 0.5
7. –
8. 0.07
9. 2, –2
10. none
11. 0.3, –0.3
8 13
8 13
12
12. , –
13. 6
14. –6
15. no real-number root
16. 0.6
17. –4
18. –4
19. –3
20. no real-number root
21. 4|x|
22. 0.5|x3|
23. x4|y9|
103
103
24. 8b24
25. –4a
26. 3y2
27. x2|y3|
28. 2y2
29. 1.34 in.
30. 1.68 ft
31. 0.48 cm
32. 0.08 mm
33. 10, –10
34. 1, –1
35. 0.5, –0.5
Lesson 7-1
3
36. , –
37. –64, 64, – –64, 64
38. a. 35 ftb. 20 ft longer
39. 0.5
40.
41. 0.2
42.
43. 2|c|
44. 3xy2 3
45. 12y2z2x xy
46. y4
23
23
13
14
3 36
3
47. –y4
48. k3
49. –k3
50. |x + 3|
51. (x + 1)2
52. |x|
53. x2
54. |x3|
55. Answers may vary. Sample:
–8x6, – 16x8, –32x10
56. a. for all positive integersb. for all odd positive integers
3 4 5
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Lesson 7-1
4
pages 371–373 Exercises
1. 16
2. 4
3. –9
4. 4
5. not possible
6. not possible
7. –6
8. 6
9. 2x 5x
10. 3 3x2
11. 5x2 2x
3
12. 2a 4a2
13. 3y3 2y
14. 10a3b3 2b
15. –5x2y 2y2
16. 2y 4x3y2
17. 2 12
18. 8y3 5y
19. 7x3y4 6y
20. 40xy 3
21. 30y2 2y
22. –2x2y 30x
23. 10
24.
25. 2x2y2 2
26. 5x3 x2y2
27.
28.
29.
30.
31.
32. 5x2 5
33.
4xy
3
3
3
3
4
3
3
2x210x
4x4x
2
2505
15y5y
45x2
3x4
3
3
Lesson 7-2
5
48.
49.
50.
51. –
52. –4 4 – 6 2
53.
54.
55. 212 mi/h greater
56. 20 22 cm2
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34.
35. r =
36. a.
b.
c. Answers may vary. Sample: First simplify the denominator. Since 98 = 2 • 49 = 7 2, to rationalize the denominator,
multiply the fraction by .
This yields =
.
x 102y
Gm1m2FF
6 + 3156 + 315
2 2
2 • 2 + 3 • 27 2 • 2
2 + 614
37. 10 2
38. 4 5
39. 3x6y5 2y
40. 20x2y3 y
41. 10 + 7 2
42. 15 + 3 21
43. 5 + 5 3
44. 2x 2
45. 3x2 x
46.
47.
3
3
3
x 10y2y 2
5 14x21x
3 3
3x2
3x
3
6 – 24
3 5 + 55
33x4x
2xy 2
xy
3
2 25xx
3
Lesson 7-2
6
pages 376–378 Exercises
1. 6 6
2. 4 3
3. cannot combine
4. –2 x
5. cannot combine
6. 5 x2
7. 33 2
8. 13 5
9. 7 2
10. 5 2
11. 9 3 – 6 23 3
3
3
3
12. 2 2 + 2 3
13. 8 + 4 5
14. 23 + 7 7
15. 63 – 38 2
16. 8 + 2 15
17. 49 + 12 13
18. 38 + 12 10
19. 14
20. 4
21. –40
22. –2
23. –2 + 2 3
4 4 24.
25. 13 + 7 3
26.
27. 13 2
28. 8 3
29. 48 2x
30. 5 3 – 4 2
31. 33y 6
32. –2 2
33. –11 + 21
34. 8 + 10
35. 17 + 31 2
3
11 + 8 2–14
12 3 + 823
Lesson 7-3
7
36. –36 – 15 2
37. x + 3 3x + 6
38. 8y – 22 2y + 30
39.
40. 2 3 – 2
41.
42.
43.
44. 2 2 – 12
45. The reciprocal is ,
which is one less than .
89 + 42 3–239
3 – 72
2 + 3 42
x + 5 x3
x
3
4
33
–1 + 52
1 + 52
46. a must be twice a perfect square.
47. 14 7 m
48. Answers may vary. Sample: Without simplifying first, you must estimate three separate square roots, and then add the estimates. If they are first simplified, then they can be combined as 13. Then only one square root need be estimated.
49. Answers may vary. Samples: ( 7 + 2)( 7 – 2); (2 2 + 5)(2 2 – 5)
50. s, or about 4.53 s
51. –
52. 4 3
60 – 20 27
12
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Lesson 7-3
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7 7
5 5
55
pages 382–384 Exercises
1. 6
2. 3
3. 7
4. 10
5. –3
6. 6
7. 8
8. 3
9. 3
10. x
11. x5
6
12
12
32
32
32
1
y98
1
y8 9
1
t 34
1
t4 3
22. a
23. a
24. c
25. 25x2y2
26. 72.8 m
27. 15.1 m
28. 7.9 m
29. 1.6 m
30. 4
31. 16
32. 4
33. 64
12
23
23
12. x2 or ( x)2
13. y2 or ( y)2
14. or
15. or
16. x3 or ( x)3
17. y6 or ( y)6
18. (–10)
19. 7 x
20. (7x)
21. (7x)
Lesson 7-4
9���
34.
35. 8
36. 64
37. 1000
38.
39.
40.
41.
42. –
43. –2y3
1 16
1 x2
1 x4
1
3x 23
5
x23
3 x3
44.
45. x
46.
47.
48. x3y9
49.
50. –7
51. –3
52. 64
53. 729
1x
y4
x3
y2
x8
y5
x10
133
54. 2,097,152
55. 1,000,000,000 or 109
56.
57.
58.
59. 16
60. –
61. 10
62. 78%, 61%, 37%
63. 635.87
64. 768
14181 36
1 81
Lesson 7-4
10���
65. x
66. y
67. x
68. y
69. x y
70.
71.
72.
73.
12
45
12
12
16
14
1
x y14
56
4x7
9y9
9y8
4x6
1
x 1336
74.
75.
76.
77. The cube root of –64 is –4,
which equals –(64) . The square root of –64 is not a real number, but
–(64) = – 64 = –8.
78. The exponent applies
only to the 5, not to the 25.
1
x 7
24
1
x13
1
(xy) 12
13
12
12
12 4 – 5
2
12
14
12
24
12
4
79. a. Answers may vary.
Sample: 4 – 5 ,
2(4 – 5 ), b. no
80. a. x • x • x • x =
x • x = x2, so x2 = x
b. x2 = (x2) = x = x = x
81. 49
82. 9
83. x2
84. 1
Lesson 7-4
11
pages 388–390 Exercises
1. 16
2. 1
3. 22
4. 4
5. 23
6.
7. 3
8. 29, –27
9. 18
10. 78
11. 8
23
12. 0
13. 30.6 ft
14. 4 in.
15. 3
16. 1
17. –3, –4
18. 9
19. 1
20. 1
21. 3
22. –2
23. 1
24. 6
25. 2
26. –2
27. 5
28. –3
29. 5
30. –2
31. s = A; 4 2 m,
or about 5.7 m
32. a. s =
b. about 8.8 in.
c. about 15.2 in.
2 3A3
Lesson 7-5
12
33. a. b. c.
d. The graph of each pair consists of two straight lines, one of which is horizontal. They intersect at different points, but these points have the same x-value, about 1.236.
34. 8
35. 4
36. 5
37. 23
38. 1
39. 5.0625
40. 6.5
41. 9, –7
42.
43. 9
44. 2
45. –1, –6
46. 2
47. 7
48. 25
49. 10
50. –1
51.
8116
54
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Lesson 7-5
13
pages 394–398 Exercises
1. x2 + 3x + 5
2. x2 – 3x – 5
3. –x2 + 3x + 5
4. 3x3 + 5x2
5.
6.
7. x2 + 3x + 5
8. –x2 + 3x + 5
9. x2 – 3x – 5
10. 3x3 + 5x2
3x + 5x2
x2
3x + 5
11.
12.
13. 2x2 + 2x – 4; domain: all real numbers
14. –2x2 + 2; domain: all real numbers
15. 2x2 – 2; domain: all real numbers
16. 2x3 – x2 – 4x + 3; domain: all real numbers
17. 2x + 3; domain: all real numbers except 1
18. ; domain: all real numbers except and 1
19. 27x2, domain: all real numbers; 3, domain: all real numbers except 0
20. 2x + 3; 9, –1
21. x2 + 5; 14, 9
3x + 5x2
x2
3x + 5
1 2x + 3
Lesson 7-6
14
Lesson 7-622. 8
23. 104
24. 20
25. 16
26. 8
27. 10
28. 12
29. 68
30. 404
31. 1
32. 25
33. –3
34. 9
35. 9.25
36. 0.25
37. 6.25
38. –2.75
39. c2 – 6c + 9
40. c2 – 3
41. a2 + 6a + 9
42. a2 – 3
43. a. ƒ(x) = 0.9xb. g(x) = x – 2000c. $14,200d. $14,400
44. a. (g °ƒ)(x) = 1.0968xb. 16.45 pesos
45. x2 – x + 7
46. 6x + 13
47. x2 – 5x – 3
48. –2x2 + 8x + 1
49. –x2 + 5x + 13
50. 2x2 + 2x + 24
51. –3x2 + 2x + 16, domain: all real numbers
52. 3x2 – 12, domain: all real numbers
53. 3x3 + 8x2 – 4x – 16, domain: all real numbers
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15
Lesson 7-6
54. –9x3 – 24x2 + 12x + 48, domain: all real numbers
55. 3x – 4, domain: all real numbers except –2
56. 15x – 20, domain: all real numbers except –2
57. 7; answers may vary. Sample: First evaluate ƒ(3) since the expression is (g °ƒ)(3), and that means g(ƒ(3)). Then evaluate g(6).
58. 1
59. –4
60. 0
61. 2
62. a. 1963; the area after 2 seconds is about 1963 in.2.
b. 7854 in.2
63. 3x2, 9x2
64. x – 2, x – 2
65. 12x2 + 2, 6x2 + 4
66. x – 3, x – 6
67. –4x – 7, –4x – 28
68. ,
69. Answers may vary. Sample:a. g(x) = 0.12xb. ƒ(x) = 9.50xc. (g ƒ)(x) = 1.14x; your savings will
be $1.14 for each hour you work.
x2 + 52
x2 + 10x + 254
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°
16
Lesson 7-7
pages 404–406 Exercises
1.
2.
3.
4.
5. y = x – ; yes
6. y = x + ; yes
7. y = – x + ; yes
8. y = y = ± no
9. y = ± x – 4; no
10. y = ± no
11. y = ± x – 1; no
12. y = ± no
13. y = ± ; no
13
13
12
12
13
43
5 – x2
x + 53
x + 42
x – 5 – 12
17
Lesson 7-714.
15.
16.
17.
18.
19.
20.
21.
22.
18
Lesson 7-723. ƒ–1(x) = , and the domain
and range for both ƒ and ƒ–1 are all real numbers; ƒ–1 is a function.
24. ƒ–1(x) = x2 + 5, x 0, domain ƒ: {x|x > 5}, range ƒ: {y|y 0}, domain ƒ–1: {x|x 0}, and range ƒ–1: {y|y 5}; ƒ–1 is a function.
25. ƒ–1(x) = x2 – 7, x 0, domain ƒ: {x|x –7}, range ƒ: {y|y 0}, domain ƒ–1: {x|x 0}, and range ƒ–1: {y|y –7}; ƒ–1 is a function.
x – 43
26. ƒ–1(x) = , x 0, domain ƒ: {x|x },
range ƒ: {y|y 0}, domain ƒ–1: {x|x 0}, and range ƒ–1: {y|y }; ƒ–1 is a function.
27. ƒ–1(x) = ± , x 2, domain ƒ: all reals,
range ƒ: {y|y > 2}, domain ƒ–1: {x|x 2}, and range ƒ–1: all reals; ƒ–1 is not a function.
28. ƒ–1(x) = ± 1 – x , x 1, domain ƒ: all reals, range ƒ: {y|y 1}, domain ƒ–1: {x|x 1}, and range ƒ–1: all reals; ƒ–1 is not a function.
3 – x2
3
x – 22
32
32
>–>–
>–>–
>–>– >–
>–>–
>–>– >–
>–>–
<–
<–
<–<– <–
19
Lesson 7-7
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3
29. a. F = (C – 32); yes
b. –3.89°F
30. a. r = ; yes
b. 20.29 ft
31. 10
32. –10
33. 0.2
34. d
35. ƒ–1(x) = ± ; no
36. ƒ–1(x) = ± 2 ; no
37. ƒ–1(x) = ± ; yes
3V4
3
2x + 83x3
x2 – 6x + 102
38. ƒ–1(x) = ± x – 1; no
39. ƒ–1(x) = ; no
40. ƒ–1(x) = –1 ± x + 1; no
41. ƒ–1(x) = x; yes
42. ƒ–1(x) = ± x; no
43. ƒ–1(x) = ± ; no
44. x = ; 25 ft, 6.25 ft
45. The range of the inverse is the domain of ƒ, which is x 1.
46. 2 and 5
5x – 52
V 2
64
1± x2
4
>–
20
Lesson 7-8pages 411–413 Exercises
1.
2.
3.
4.
5.
6.
7.
8.
9.
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21
Lesson 7-810.
11.
12.
13.
14.
15.
16.
17.
18.
��
22
Lesson 7-819.
20.
21.
22.
23. a.
b. 745 ft, 1053 ft, 1343 ft24.
25.
26.
27.
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