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2. Consider the functions: • f : Z+ → Z+ defined via: f(n) = n¹ +1 • g : (Z+ − {1}) → Z+ defined via: g(n) is the smallest integer m s.t. m ≥ 2 and m❘n. For example: g(2) 9(35) = 5. = 2, g(3) = 3, g(6) = 2, g(7) = 7, g(8) == 2, g(9) = 3, (a) Compute is go f(2) and go f(3). There is no need to justify. (b) Is f one-to-one? Onto? Invertible? justify! (c) Is g one-to-one? Onto? Invertible? justify!

2. Consider the functions: • f : Z+ → Z+ defined via: f(n) = n¹ +1 • g : (Z+ − {1}) → Z+ defined via: g(n) is the smallest integer m s.t. m ≥ 2 and m❘n. For example: g(2) 9(35) = 5. = 2, g(3) = 3, g(6) = 2, g(7) = 7, g(8) == 2, g(9) = 3, (a) Compute is go f(2) and go f(3). There is no need to justify. (b) Is f one-to-one? Onto? Invertible? justify! (c) Is g one-to-one? Onto? Invertible? justify!

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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2. Consider the functions: • f : Z+ → Z+ defined via: f(n) = n¹ +1 • g : (Z+ − {1}) → Z+ defined via: g(n) is the smallest integer m s.t. m ≥ 2 and m❘n. For example: g(2) 9(35) = 5. = 2, g(3) = 3, g(6) = 2, g(7) = 7, g(8) == 2, g(9) = 3, (a) Compute is go f(2) and go f(3). There is no need to justify. (b) Is f one-to-one? Onto? Invertible? justify! (c) Is g one-to-one? Onto? Invertible? justify!
Transcribed Image Text:2. Consider the functions: • f : Z+ → Z+ defined via: f(n) = n¹ +1 • g : (Z+ − {1}) → Z+ defined via: g(n) is the smallest integer m s.t. m ≥ 2 and m❘n. For example: g(2) 9(35) = 5. = 2, g(3) = 3, g(6) = 2, g(7) = 7, g(8) == 2, g(9) = 3, (a) Compute is go f(2) and go f(3). There is no need to justify. (b) Is f one-to-one? Onto? Invertible? justify! (c) Is g one-to-one? Onto? Invertible? justify!
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