(a) Are the following functions surjective? Justify your answers. (i) The function a : Z→ Z defined by a(n) = 3n+ 1. (ii) The function b: ZxZ→ Z defined by b(m, n) = 3m + n. (iii) The function c: N→ N defined by c(n) = the number of digits of n². (b) Let f: Z→ Z be defined by f(n) = 3n+2. Find a function g: Z → Z such that g of is the identity function on N. (c) Is g an inverse for f? Justify your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Are the following functions surjective? Justify your answers.
(i) The function a : Z→ Z defined by a(n) = 3n+ 1.
(ii) The function b: Zx Z→ Z defined by b(m, n) = 3m + n.
(iii) The function c: N→ N defined by c(n) = the number of digits of n².
(b) Let f: Z→ Z be defined by f(n) = 3n+2. Find a function g: Z→ Z such that g of is the
identity function on N.
(c) Is g an inverse for f? Justify your answer.
Transcribed Image Text:(a) Are the following functions surjective? Justify your answers. (i) The function a : Z→ Z defined by a(n) = 3n+ 1. (ii) The function b: Zx Z→ Z defined by b(m, n) = 3m + n. (iii) The function c: N→ N defined by c(n) = the number of digits of n². (b) Let f: Z→ Z be defined by f(n) = 3n+2. Find a function g: Z→ Z such that g of is the identity function on N. (c) Is g an inverse for f? Justify your answer.
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