Find sets a b c and functions f a b and g b c such

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9. Find sets A, B, C and functions f: A B and g: B C such that a) f is onto B, but g οf is not onto C. Let f: R R be given by f(x) = x and g: R R be given by g(x) = x3+ 1. Thus f maps onto R, but g οf is not onto R. b) g is onto C, but g οf is not onto C. Let f: R R be given by f(x) = x3and g: R R be given by g(x) = 2x + 1. Thus g maps onto C, but g οf is not onto C. c) g οf is onto C, but f is not onto B. Let f: R R be given by f(x) = x3and g: R N be given by g(x) = 2x + 1. Thus g οonto C, but f is not onto B. d) f is one-to-one, but g οf is not one-to-one. Let A = { 1, 2, 3 }, B = { 4, 5, 6 }, C = { a, b, c }. Suppose f = { (1,4), (2,5), (3,6) } and g = { (4,a), (5,a), (6,a) }. Thus f is one-to-one, but g οf is not one-to-one. e) g is one-to-one, but g οf is not one-to-one. Let A = { 1, 2, 3 }, B = { 4, 5, 6 }, C = { a, b, c }. Suppose f = { (1,4), (2,3), (3,6) } and g = { (4,a), (5,b), (6,c) }. Thus g is one-to-one, but g οf is not one-to-one. f) g οf is one-to-one, but g is not one-to-one. Let A = { 1, 2, 3 }, B = { 4, 5, 6, 7 }, C = { a, b, c }. Suppose f = { (1,4), (2,5), (3,6) } and g = { (4,a), (5,b), (6,c), (7,a) }. Thus g οf is one-to-one, but g is not one-to-one.
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Joshua Parker Homework – Week 11 Submission Math – M393 5 Section 4.4

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