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1. Let A = {1,2,3}, B = {4,5,6}, C = {7,8,9,10}. C are defined by f(3) = 7, The functions f : AC and g: B f(1) = 7, f(2) = 9, g(4) = 10, Does there exist a function h: A → B such that go h = f? Does there exist a function k: B→ A such that fok = g? Justify your answers. g(5) = 7, g(6) = 9.

1. Let A = {1,2,3}, B = {4,5,6}, C = {7,8,9,10}. C are defined by f(3) = 7, The functions f : AC and g: B f(1) = 7, f(2) = 9, g(4) = 10, Does there exist a function h: A → B such that go h = f? Does there exist a function k: B→ A such that fok = g? Justify your answers. g(5) = 7, g(6) = 9.

Advanced Engineering Mathematics
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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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.
Transcribed Image Text: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.
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