Select the following statements that are true.ΟΣ, .j=C(n+1,2)2161-21[13]4=1 + 1 + 1 +The function f(x) = 1³-2 2+ = 2.2™= [³/7] isis an one-to-one correspondence from Z to Z.Olff: A→ Bis a function from a set A of cardinality 26 to a set B ofcardinality 25, then f is not one-to-one.

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Answered: =C(n+1,2) °2161-41 [13] = ... 01+++ The…

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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7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the stated conditions, or explain why no such example exists. * (a) The function f is a surjection, but the function gof is not a surjection. * (b) The function f is an injection, but the function gof is not an injection. (c) The function g is a surjection, but the function g of is not a surjection. (d) The function g is an injection, but the function go ƒ is not an injection. (e) The function f is not a surjection, but the function gof is a surjection. * (f) The function f is not an injection, but the function gof is an injection. (g) The function g is not a surjection, but the function gof is a surjection. (h) The function g is not an injection, but the function gof is an injection.
Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers. Consider a function f: N² → N given by f((a, b)) = a + b. a. Let A = {(a, b) E N²: a, b ≤ 10}. Find f(A). b. Find f-1 (3) and f-¹({0,1,2,3}). c. Give geometric descriptions of f-1 (n) and f-¹({0,1,...,n}) for any n ≥ 1. d. Find f¹(8) and f-¹({0,1,...,8}).
3. Assume f:{-3, 0, 2, 11} → {-11, 0, 3, 5, 19} be a function given by f(-3) = 0, f(0) = -11,f(2)= 5, f(11) = 19. Determine the following: a) Domain f) b) Co-domain g) h) c) Range d) Image of 3 e) Pre-image of 2 Is f one-one? Is f on-to? Is f one-one corresponding, if so, find the inverse?
The circular convolution of f [n] = [1,–2,3] with g[n] = [-4, 5, –6] is: A- [-4, 13, –28, 27, – 18]; B- [-4, –10, – 18]; C- [23, –5, –28]; D- None of the above.
A function f: {1,2,3,4} is defined by f(1) = 6, ƒ(2) = 7, f(3) = 8, ƒ(4) = 6. Drag the answers into the right place for the following questions ƒ({3,4}) = ƒ¯¹({5,8}) = ƒ(ƒ˜¯¹({7,8})) = ƒ˜¹ (ƒ({1,3})) =| {4} {5,6,7,8} {1,3,4} {8} {7,8} {6,8} {3,4} {5,6} {5,6,7,8} {2,3} {3} {6} {1,3}
= mx + b. 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x) A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (−1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. =
1. Let A = {1,2,3}, B = B = {4,5,6}, The functions f : A → C and g: B → C are defined by f(1) = 7, f(2)= 9, f(3) = 7, Does there exist a function h: A → B such that go h = f? Does there exist a function k : B → A such that fo k = g? Justify your answers. {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.
{1,5,10,15} and Y1 = {1,5,10,15,20}. Using the formal definition of a function, determine which of the following subsets of X1 × Y 1 correspond to the functions of X1 → Y 1. Justify your Problem 7. Let X1 = answer by providing reasons why each is or is not a function. 7(a) f = {(1,15),(5,10),(1,5),(10,1),(15,1)} 7(b) f = {(1,20),(5,1),(10,1),(15,5),(1,20)} 7(c) f = {(1,1),(5,1),(10,1)}

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=C(n+1,2) °2161-41 [13] = ... 01+++ The function f(x) = [37] is an one-to-one correspondence from Z to Z. Olff: A → B is a function from a set A of cardinality 26 to a set B of cardinality 25, then f is not one-to-one. -1 21 +2 = 2-2