Let N = {1,2, 3, ...}. Are the following functions injective, surjective and/or bijec- tive? (i) ƒ: N → N, f(n) = 2n; (ii) f: N → N, f(n) = 2"; (iii) f: N → N, f (n) = number of all positive divisors of n. Let N = {1, 2, 3,...} and let f: N → N be a function given by f(x) = 2x + 3. (i) Find f(f(4) +1). (ii) Find f({1,2, 3, 4, 5}). (iii) Find f-'({1, 2, 3, 4, 5, 6, 7, 8, 9, 10}). (iv) Is f injective? (v) Is f surjective?
Let N = {1,2, 3, ...}. Are the following functions injective, surjective and/or bijec- tive? (i) ƒ: N → N, f(n) = 2n; (ii) f: N → N, f(n) = 2"; (iii) f: N → N, f (n) = number of all positive divisors of n. Let N = {1, 2, 3,...} and let f: N → N be a function given by f(x) = 2x + 3. (i) Find f(f(4) +1). (ii) Find f({1,2, 3, 4, 5}). (iii) Find f-'({1, 2, 3, 4, 5, 6, 7, 8, 9, 10}). (iv) Is f injective? (v) Is f surjective?
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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Transcribed Image Text:Let N = {1,2, 3, ...}. Are the following functions injective, surjective and/or bijec-
tive?
(i) ƒ: N → N, f(n) = 2n;
(ii) f: N → N, f(n) = 2";
(iii) f: N → N, f (n) = number of all positive divisors of n.
Transcribed Image Text:Let N = {1, 2, 3,...} and let f: N → N be a function given by
f(x) = 2x + 3.
(i) Find f(f(4) +1).
(ii) Find f({1,2, 3, 4, 5}).
(iii) Find f-'({1, 2, 3, 4, 5, 6, 7, 8, 9, 10}).
(iv) Is f injective?
(v) Is f surjective?
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