9. 3
11. −3−3
13. −4−4
15. 1212
17. 1
19. 0
21.
(f+g)(−1)=−1(f+g)(−1)=−1
(f−g)(0)=0(f−g)(0)=0
(f⋅g)(2)=−8(f⋅g)(2)=−8
(fg)(1)=−2(fg)(1)=−2
23.
(f+g)(−1)=0(f+g)(−1)=0
(f−g)(0)=12(√2−2)(f−g)(0)=12(2–√−2)
(f⋅g)(2)= 52(f⋅g)(2)= 52
(fg)(1)= 13√3(fg)(1)= 133–√
25.
(f+g)(x)=x2+x−3;(f+g)(x)=x2+x−3; domain: (−∞, ∞)(−∞, ∞)
(f−g)(x)=−x2+x−3;(f−g)(x)=−x2+x−3; domain: (−∞, ∞)(−∞, ∞)
(f⋅g)(x)=x3−3x2;(f⋅g)(x)=x3−3x2; domain: (−∞, ∞)(−∞, ∞)
(fg)(x)=x−3x2 ;(fg)(x)=x−3x2 ; domain: (−∞, 0)∪(0, ∞)(−∞, 0)∪(0, ∞)
(gf)(x)=x2x−3 ;(gf)(x)=x2x−3 ; domain: (−∞, 3)∪(3, ∞)(−∞, 3)∪(3, ∞)
27.
(f+g)(x)=x3+2x2+4;(f+g)(x)=x3+2x2+4; domain: (−∞, ∞)(−∞, ∞)
(f−g)(x)=x3−2x2−6;(f−g)(x)=x3−2x2−6; domain: (−∞, ∞)(−∞, ∞)
(f⋅g)(x)=2x5+5x3−2x2−5;(f⋅g)(x)=2x5+5x3−2x2−5; domain: (−∞, ∞)(−∞, ∞)
(fg)(x)=x3−12x2+5;(fg)(x)=x3−12x2+5; domain: (−∞, ∞)(−∞, ∞)
(gf)(x)=2x2+5x3−1;(gf)(x)=2x2+5x3−1; domain: (−∞, 1)∪(1, ∞)(−∞, 1)∪(1, ∞)
29.
(f+g)(x)=2x+√x−1;(f+g)(x)=2x+x−−√−1; domain: [0, ∞)[0, ∞)
(f−g)(x)=2x−√x−1;(f−g)(x)=2x−x−−√−1; domain: [0, ∞)[0, ∞)
(f⋅g)(x)=2x√x−√x;(f⋅g)(x)=2xx−−√−x−−√; domain: [0, ∞)[0, ∞)
(fg)(x)=2x−1√x;(fg)(x)=2x−1x−−√; domain: (0, ∞)(0, ∞)
(gf)(x)=√x2x−1;(gf)(x)=x−−√2x−1; domain: [0, 12)∪(12, ∞)[0, 12)∪(12, ∞)
31. (f+g)(x)=x−6+√x−3;Domain [3, ∞)(f−g)(x)=x−6−√x−3;Domain [3, ∞)(f⋅g)(x)=(x−6)√x−3;Domain [3, ∞)(fg)(x)=(x−6)/√x−3;Domain [3, ∞)(gf)(x)=√x−3/(x−6);Domain [3, 6]∪(6, ∞)(f+g)(x)=x−6+x−3−−−−−√;(f−g)(x)=x−6−x−3−−−−−√;(f⋅g)(x)=(x−6)x−3−−−−−√;(fg)(x)=(x−6)/x−3−−−−−√;(gf)(x)=x−3−−−−−√/(x−6);Domain [3, ∞)Domain [3, ∞)Domain [3, ∞)Domain [3, ∞)Domain [3, 6]∪(6, ∞)
33.
(f+g)(x)=1−2x+1+1x=x2+1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)(f+g)(x)=1−2x+1+1x=x2+1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)
(f+g)(x)=1−2x+1−1x=x2−2x−1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)(f+g)(x)=1−2x+1−1x=x2−2x−1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)
(f⋅g)(x)=(1−2x+1)⋅(1x)=x−1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)(f⋅g)(x)=(1−2x+1)⋅(1x)=x−1(x+1)x;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)
(fg)(x)=1−2x+11x=(x−1)xx+1;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)(fg)(x)=1−2x+11x=(x−1)xx+1;Domain (−∞,−1)∪(−1, 0)∪(0, ∞)
(gf)(x)=1x1−2x+1=x+1(x−1)x;Domain (−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)(gf)(x)=1x1−2x+1=x+1(x−1)x;Domain (−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)
35.
(f+g)(x)=2+xx+1;(f+g)(x)=2+xx+1; domain: (−∞,−1)∪(−1, ∞)(−∞,−1)∪(−1, ∞)
(f−g)(x)=2−xx+1;(f−g)(x)=2−xx+1; domain: (−∞,−1)∪(−1, ∞)(−∞,−1)∪(−1, ∞)
(f⋅g)(x)=2x(x+1)2;(f⋅g)(x)=2x(x+1)2; domain: (−∞,−1)∪(−1, ∞)(−∞,−1)∪(−1, ∞)
(fg)(x)=2x;(fg)(x)=2x; domain: (−∞,−1)∪(−1, 0)∪(0, ∞)(−∞,−1)∪(−1, 0)∪(0, ∞)
(gf)(x)=x2;(gf)(x)=x2; domain: (−∞,−1)∪(−1, ∞)(−∞,−1)∪(−1, ∞)
37.
(f+g)(x)=x3−x2+2xx2−1;(f+g)(x)=x3−x2+2xx2−1; domain: (−∞,−1)∪(−1, 1)∪(1, ∞)(−∞,−1)∪(−1, 1)∪(1, ∞)
(f−g)(x)=x2−2xx−1;(f−g)(x)=x2−2xx−1; domain: (−∞,−1)∪(−1, 1)∪(1, ∞)(−∞,−1)∪(−1, 1)∪(1, ∞)
(f⋅g)(x)=2x3x3+x2−x−1;(f⋅g)(x)=2x3x3+x2−x−1; domain: (−∞,−1)∪(−1, 1)∪(1, ∞)(−∞,−1)∪(−1, 1)∪(1, ∞)
(fg)(x)=x2−x2;(fg)(x)=x2−x2; domain: (−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)(−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)
(gf)(x)=2x2−x;(gf)(x)=2x2−x; domain: (−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)(−∞,−1)∪(−1, 0)∪(0, 1)∪(1, ∞)
39.
[1, 5]
[1, 5)
41.
[−2, 3][−2, 3]
[−2, 3)[−2, 3)
43. g(f(x))=2x2+1; g(f(2))=9; g(f(−3))=19g(f(x))=2x2+1; g(f(2))=9; g(f(−3))=19
45. 11
47. 31
49. −5−5
51. 4c2−54c2−5
53. 8a2+8a−18a2+8a−1
55. 7
57. 110−5x; (− ∞, 2)∪(2, ∞)110−5x; (− ∞, 2)∪(2, ∞)
59. √2x−8; [4, ∞)2x−8−−−−−√; [4, ∞)
61. 2xx+1;(−∞,−1)∪(−1, 0)∪(0, ∞)2xx+1;(−∞,−1)∪(−1, 0)∪(0, ∞)
63. √−3x−1;(−∞,−13]−3x−1−−−−−−−√;(−∞,−13]
65. |x2−1|;(−∞, ∞)∣∣x2−1∣∣;(−∞, ∞)
67.
(f∘g)(x)=2x+5;(f∘g)(x)=2x+5; domain: (−∞, ∞)(−∞, ∞)
(g∘f)(x)=2x+1;(g∘f)(x)=2x+1; domain: (−∞, ∞)(−∞, ∞)
(f∘f)(x)=4x−9;(f∘f)(x)=4x−9; domain: (−∞, ∞)(−∞, ∞)
(g∘g)(x)=x+8;(g∘g)(x)=x+8; domain: (−∞, ∞)(−∞, ∞)
69.
(f∘g)(x)=−2x2−1;(f∘g)(x)=−2x2−1; domain: (−∞, ∞)(−∞, ∞)
(g∘f)(x)=4x2−4x+2;(g∘f)(x)=4x2−4x+2; domain: (−∞, ∞)(−∞, ∞)
(f∘f)(x)=4x−1;(f∘f)(x)=4x−1; domain: (−∞, ∞)(−∞, ∞)
(g∘g)(x)=x4+2x2+2;(g∘g)(x)=x4+2x2+2; domain: (−∞, ∞)(−∞, ∞)
71.
(f∘g)(x)=8x2−2x−1;(f∘g)(x)=8x2−2x−1; domain: (−∞, ∞)(−∞, ∞)
(g∘f)(x)=4x2+6x−1;(g∘f)(x)=4x2+6x−1; domain: (−∞, ∞)(−∞, ∞)
(f∘f)(x)=8x4+24x3+24x2+9x;(f∘f)(x)=8x4+24x3+24x2+9x; domain: (−∞, ∞)(−∞, ∞)
(g∘g)(x)=4x−3;(g∘g)(x)=4x−3; domain: (−∞, ∞)(−∞, ∞)
73.
(f∘g)(x)=x;(f∘g)(x)=x; domain: [0, ∞)[0, ∞)
(g∘f)(x)=|x|;(g∘f)(x)=|x|; domain: (−∞, ∞)(−∞, ∞)
(f∘f)(x)=x4;(f∘f)(x)=x4; domain: (−∞, ∞)(−∞, ∞)
(g∘g)(x)=√4x;(g∘g)(x)=4x−−√; domain: [0, ∞)[0, ∞)
75.
(f∘g)(x)=−x2x2−2;(f∘g)(x)=−x2x2−2; domain: (−∞,−√2)∪(−√2, 0)∪(0, √2)∪(√2, ∞)(−∞,−2–√)∪(−2–√, 0)∪(0, 2–√)∪(2–√, ∞)
(g∘f)(x)=(2x−1)2;(g∘f)(x)=(2x−1)2; domain: (−∞, 12)∪(12, ∞)(−∞, 12)∪(12, ∞)
(f∘f)(x)=−2x−12x−3;(f∘f)(x)=−2x−12x−3; domain: (−∞, 12)∪(12, 32)∪(32, ∞)(−∞, 12)∪(12, 32)∪(32, ∞)
(g∘g)(x)=x4;(g∘g)(x)=x4; domain: (−∞, 0)∪(0, ∞)(−∞, 0)∪(0, ∞)
77.
(f∘g)(x)=√√4−x−1;(f∘g)(x)=4−x−−−−−√−1−−−−−−−−−√; domain: (−∞, 3](−∞, 3]
(g∘f)(x)=√4−√x−1;(g∘f)(x)=4−x−1−−−−−√−−−−−−−−−√; domain: [1, 17][1, 17]
(f∘f)(x)=√√x−1−1;(f∘f)(x)=x−1−−−−−√−1−−−−−−−−−√; domain: [2, ∞)[2, ∞)
(g∘g)(x)=√4−√4−x;(g∘g)(x)=4−4−x−−−−−√−−−−−−−−−√; domain: [−12, 4][−12, 4]
79.
(f∘g)(x)=−7/(3x−5)(f∘g)(x)=−7/(3x−5) Domain (−∞, 5/3)∪(5/3, 4)∪(4, ∞)(−∞, 5/3)∪(5/3, 4)∪(4, ∞)
(g∘f)(x)=−(2x+7)/(5x+7)(g∘f)(x)=−(2x+7)/(5x+7) Domain (−∞,−2)∪(−2,−7/5)∪(−7/5, ∞)(−∞,−2)∪(−2,−7/5)∪(−7/5, ∞)
(f∘f)(x)=(2x+1)/(x+5)(f∘f)(x)=(2x+1)/(x+5) Domain (−∞,−5)∪(−5,−2)∪(−2, ∞)(−∞,−5)∪(−5,−2)∪(−2, ∞)
(g∘g)(x)=−(4x−9)/(3x−19)(g∘g)(x)=−(4x−9)/(3x−19) Domain (−∞, 4)∪(4, 19/3)∪(19/3, ∞)(−∞, 4)∪(4, 19/3)∪(19/3, ∞)
81. f(x)=√x; g(x)=x+2f(x)=x−−√; g(x)=x+2
83. f(x)=x10; g(x)=x2−3f(x)=x10; g(x)=x2−3
85. f(x)=1x; g(x)=3x−5f(x)=1x; g(x)=3x−5
87. f(x)=3√x; g(x)=x2−7f(x)=x−−√3; g(x)=x2−7
89. f(x)=1|x|; g(x)=x3−1f(x)=1|x|; g(x)=x3−1
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