Answered: 6. Is the function h: Z → Z defined by…

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6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

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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A(1, 1) The following function was defined by Ackermann. A(0, n) = n + 1 for all nonnegative intergers n A(m, 0) = A(m - 1,1) for all positive integers m A(m, n) = A(m - 1, A(m, n - 1)) for all positive integers m and n. Find A(1, 1). write down all intermediate steps to justify final answer.
5. Let f: CC be the function defined by f(z) = 25 for any z = C. Fill in the blanks in the blocks below, all labelled by capital-letter Roman numerals, with appropriate words so that they give respectively a proof for the statement (E) and a proof for the statement (F). (The 'underline' for each blank bears. no definite relation with the length of the answer for that blank.) (a) Here we prove the statement (E): (E) The function f is surjective. [We want to verify the statement (II) For this C, (IV) By definition, z E C. Note that f(z) = 2 = It follows that (VI) (b) Here we prove the statement (F): (F) The function f is not injective. (III) [We want to verify the statement (II) Note that zo, wo E C. Also note that We have (IV) and It follows that (VI) (III) (V) (1) 9 such that CC(cos(0) + sin(0)). (1) (V) Then f(zo) f(wo).
4. (a) Let a Z→→ Z be the function defined by a(n) = 2n + 1, and let i: Z→ Z be the identity function. Is there a function b: Z→ Z such that bo a = i? Is there a function b: Z→ Z such that a ob=i? (b) Let f: N N and g: N→ N be defined by f(n) = n + 1, n-1 g(n) = 1 Find the functions fog, gof, fogof and gofog. if n > 1 if n = 1.
Please help me with these questions. I
7. Consider the function f: N → N given by f(n) (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer. ( n/2, if n is even (3n + 1, if n is odd
5. Consider the function f! NXN → N., defined by f(m,n) = Min +1
1. Let f: N→ N be a rule defined by n f(n) = 2 if n > 1 2n + 1 ifn ≤ 1 (a) Is f a well-defined function? Justify your answer. *Well-defined function: the function applies to all in the domain, outputs are all in codomain, inputs have one single output. (b) What is the domain and codomain of this function? Justify your answer. *Domain - set of all inputs for a function/ Codomain - set of all possible outputs/ Range - outputs of f for some input x (c) Is this function injective, surjective, or bijective? Justify your answer.
10. Let F : R" → R™ and g : R" → R. Prove that d(gF)[a; h] = g(a)dF[a; h] + F(a)dg[a; h].
6.3) If f = u + iv is non-constant and analytic in an open set U, which one of the following are analytic as well? (a) g = u - iv, (b) h = v +iu, (c) k = -u -iv, (d) l= iu - v.
3. Let S {1,2, 3, 4} and define functions f,g : S → S by f = {(1,3), (2,2), (3, 4), (4, 1)} and g = {(1, 4), (2, 3), (3, 1), (4, 2)}. Find (a) g-1 o f og (b) f oglog (c) f-1 og –1 -1ofog
Please help me with these questions. I am having trouble understanding what to do. Please show all your work on paper SUBJECT: Discrete mathematics Thank you
Please help. I am having trouble understanding what to do for these questions. Please show your work Thank you