52 lines
1.0 KiB
Plaintext
52 lines
1.0 KiB
Plaintext
1. a) f(x) is undefined for x = 0
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b) f(x) is complex for x < 0
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c) multivalued
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2. a) multivalued
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b) It is
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c) undefined at x = 2
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3. a) Z >= 0, {0..9}
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b) 0.. -> 1..?
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c) All bit strings -> N
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d) All bit strings -> N
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e) (Z^+)^2 -> Z^+
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f) (Z^+)^2 -> Z^+
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4. a) 1 b) 2 c) -1 d) 0 e) 2 f) 3 g) 0 h) 2
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5. a) 1 b) 0 c) 0 d) -1 e) 3 f) -1 g) 2 h) 1
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8. a) 6 b) 24 c) 120 d) 3_628_800
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10. a)y b)n c)n
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11. {a}
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12. a) y b) n c) n d) n
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13. a) y b) n) c) y) d) n
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14. ynyy
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15. a) everyone has a phone number (phone numbers should already be uniquie)
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b) None (student ids should already be unique)
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c) Every student gets a unique grade
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d) no two people come from the same town
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16. a) the set of phone numbers
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b) the set of student ids
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c) 1..100
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d) all towns
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17. ynnn
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18. a) { 1 }
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b) { -1, 1, 5, 9, 15 }
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c) { 0, 1, 2 }
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d) { 0, 1, 2 }
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19. f.g = x^2 + 4x + 5, g.f = x^2 + 3
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20. f + g = x^2 + x + 3
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fg = x^3 + 2x^2 + x + 2
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21. f^-1 doesn't exist, assuming f^-1(x) = +sqrt(x)
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a) { 1 }
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b) { x | 0 < x < 1 }
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c) { x | x > 2 } |