3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondencebetween (a, b) and (c, d). Make sure to explain why the function you found is bothone-to-one and onto.

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Answered: 3. Let a, b, c, d be real numbers with…

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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19. Which relation is not a function? A. (1, -5) (2,-4) (1,-4) B. (1,-5) (2,-4) (3,-3) C (1, -5) (2,-4) (3, 2) D. (1, -5) (2,-4) (3,-4)
Assume that T is a linear transformation. Find the standard matrix of T.
3. For each of the following relations: a. Is it a function? Explain. b. State the domain and range. i) y 3. 2. X 2 3 5 6
3. Write the conjunctive function.
Which of the following set is not a function? a. D = {(8,2), (-1,5), (-5,2), (5,0)} b. B = {(3,2), (1,5), (-4,2), (5,0)} C. Z = {(-3,2), (1,5), (-3,2), (1,0)} d. A = {(3,2), (7,4), (-7,2), (5,0)}
Which of the following is a function one-one from the set A = {1,2,3} to B = {4,5,6} is: (Explain) A. {(1,4), (2,5), (3,4)} B. {(1,6), (2,4), (3,4)} C. {(3,5), (2,4), (1,5)} D. {(3,4),(2,5),(1,6)}
Decide whether the following relation defines a function. ((5,3), (4,3), (5,2)} Is the set of ordered pairs a function? Yes No
2. Does this relation represent a function? {(3,-5), (1, -6), (3, -7), (8, -3)} Yes No
1. Determine if the set or relation forms a function. (a){(-2, 1), (2, 2), (-1, 2), (1, 2), (0, 2), (4, 2)} (b){(1, 2), (–3, 10), (0, 0), (4, 12), (–2, 0)}. (c){(-1, 1), (–2, 4), (10, 8), (-1, 0), (4, 20), (3, 5)}
Let R be the relation with ordered pairs (Abdul, 22), (Brenda, 24), (Carla, 21), (Desire, 22), (Eddie, 24), and (Felicia, 22). Here each pair consists of a graduate student and this student’s age. Specify a function determined by this relation.
Diagonalize the following matrix with a similarity transformation: [5 7 -51 0 4 -1 L2 8 -3] A: = Functions of Diagonaligal
Determine whether each of the following is a function or a relation. a. {(-1,8),(0,15), (1,-4), (2,0)} b. {(-5,2), (5,2), (0,-3), (3,-8)} c. {(-2,7), (6,2), (-2-3). (0,9)} d. {(7,2),(4,-6), (2,-2).(4,-9)} е. {(2,3), (2,4), (2,5), (2,6)} f. {(1-4), (2,-4), (3,-4), (3,-4)} Answer: Function Answer: Function Answer: Relation Answer: Function Answer: Relation Answer: Relation

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3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a, b) and (c, d). Make sure to explain why the function you found is both one-to-one and onto.