Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C 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 fok = g? Justify your answers. {4,5,6}, {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let
A = {1,2,3},
B
B =
Define the functions f: A→ C and g: B → C 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 fok = g?
Justify your answers.
= {4,5,6},
{4,5,6}, C = {7, 8, 9, 10}.
g(4) = 10,
g(5) = 7,
g(6) = 9.
Transcribed Image Text:Let A = {1,2,3}, B B = Define the functions f: A→ C and g: B → C 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 fok = g? Justify your answers. = {4,5,6}, {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.
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