Determine which is a function from x to y.1. {(d,a), (a.a), (e,b), (b,c)} 2. {(2,1), (5,2), (5,3), (6,4)} Determine which is a function from x to y.{(d,a), (a.a), (e,b), (b,c)}{(2,1), (5,2), (5,3), (6,4)}

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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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alfa & OIa" +| 2:49 PM Let X = {a, b, c, d} and TX = {ø, X, {b}, {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3, 4} and TY = {Ø, Y, {3}, {1,2,3}} be a topology on Y. Let f be a mapping from X into Y defined by f(a)=f(b) = 3, f(c) = 2 and f(d) = 1. Let g be mapping from X into Y defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 2. Then f is continuous and g is not continuous f is not continuous and g is continuous f and g are not continuous f and g are both continuous < O O ...
Determine if the following relations describe a function. Justify your answer. a.) R₁ = {(-2,0), (-2,1), (1,1), (5,2), (7,5)} b.) R₂ = {(x,y) y=x+1}
What is the smallest number that can be represented as the sum of four positive squares (not necessarily unique) in two different ways?
a. 9 b. 7 c. 4 d. 5
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11. Which of the following relations is a function? А. ((9,4), (-7, -4), (3, —5), (-3, 5)} {(2, 1), (8, 7), (5, –9), (8, –4)} С. (6, -4), (0, -2), (0,—1), (6, 3)} D. ((3, 1), (4, 5), (0,–2), (4, -1)} pag
Which sets of ordered pairs represent functions from A to B? (Select all that apply.) A = {a, b, c} and B = {12, 13, 14, 15} {(a, 13), (c, 14), (c, 15)(b, 15)} {(13, a), (12, a), (14, c), (15, b)} {(a, 13), (b, 14), (c, 15)}
. Let f= {(-4,4), (-2, 4), (1, 3), (3, 5), (4, 6)} and g= {(-4, 2), (2, 1), (0, 2), (1, 2), (2, 2), (4,4)}. Determine: a) g-f
2. (AKS 36) Which of the following tables does not represent a function? A. B. -9 -5 -9 2. -9 -1 -1 6. 2. 2. -9 -2 -9 -2 -5 -2 2-5 9. 24 1.
C. State whether or not the following relations are functions. Also, give their domain and range. 1) S = {(1, 1), (2,1), (3,1)} 2) T = {(a, 5), (e, 5), (u, 6), (e, 6)} = {((1,2), 3), ((2,1), 4), ((1,3),4)} 3) R = 4) 0 = {(x,y) y = } = {(x,y) y = √4x²} 6) G = {(x, y) ly = |x + 1|} 5) N =
Which of the following relations does not represent a function? {(1, 2), (2, 2), (3, 2)} В. ((1, 1), (2, 2), (3,3)) С. ((1,1), (1, 2), (1,3)} D. {(1, 1), (2, 1), (3,1)}

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Determine which is a function from x to y. {(d,a), (a.a), (e,b), (b,c)} {(2,1), (5,2), (5,3), (6,4)}