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Determine whether cach of these functions from Z to Z is one-to-one. a) f(n)=n- I c) f(n)=n b) f(n) = n² + 1 d) f(n) = [n /2] 71 Whieh

Determine whether cach of these functions from Z to Z is one-to-one. a) f(n)=n- I c) f(n)=n b) f(n) = n² + 1 d) f(n) = [n /2] 71 Whieh

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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d) - e) [31 h) -11 10. Determine whether cach of these functions from (a, b.c, d) to itself is one-to-one. a) f(a) b, f(b)=a, f(c) = c, f (d) = d b) f(a)b, f(b)=b. f(c) = d, f(d) = c e) f(a) d, f(b)=b, f(c) = c, f(d) = d 7. 11. Which functions in Excrcise 10 are onto? 12. Determine whether cach of these functions from Z to Z is one-to-one. a) f(n)=n c) f(n) = b) f(n) = n2 + 1 d) f(n)= [n/21 13. Which functions in Exercise 12 are onto? 14. Determine whether Z × Z a) f(m, n) = 2m -n. b) f(m, n): c) f(m, n) =m +n + 1. d) f(m, n) = m- (2 e) f(m, n) = m² – 4. 15. Determine whether the function f: Z x Z Z is onto Z is onto if wwww. %3D if 25 a) f(m, n) =m+n. b) f(m, n) = m2 +n2. c) f(m, n) = m. d) f(m, n)= In. e) f(m, n) m-n. 16. Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her a) mobile phone numher %3D 26. 27. a
Transcribed Image Text:d) - e) [31 h) -11 10. Determine whether cach of these functions from (a, b.c, d) to itself is one-to-one. a) f(a) b, f(b)=a, f(c) = c, f (d) = d b) f(a)b, f(b)=b. f(c) = d, f(d) = c e) f(a) d, f(b)=b, f(c) = c, f(d) = d 7. 11. Which functions in Excrcise 10 are onto? 12. Determine whether cach of these functions from Z to Z is one-to-one. a) f(n)=n c) f(n) = b) f(n) = n2 + 1 d) f(n)= [n/21 13. Which functions in Exercise 12 are onto? 14. Determine whether Z × Z a) f(m, n) = 2m -n. b) f(m, n): c) f(m, n) =m +n + 1. d) f(m, n) = m- (2 e) f(m, n) = m² – 4. 15. Determine whether the function f: Z x Z Z is onto Z is onto if wwww. %3D if 25 a) f(m, n) =m+n. b) f(m, n) = m2 +n2. c) f(m, n) = m. d) f(m, n)= In. e) f(m, n) m-n. 16. Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her a) mobile phone numher %3D 26. 27. a
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