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Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it is not. (a) g: C→C defined by g(z) = 2² +1. (b) g: C\ {0} → C defined by g(z) = 2¹.

Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it is not. (a) g: C→C defined by g(z) = 2² +1. (b) g: C\ {0} → C defined by g(z) = 2¹.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 1E: Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary...
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Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it is not. (a) g: C→C defined by g(z) = z² + 1. (b) g: C\ {0} → C defined by g(z) = 2¹. (c) g: C\ {1} → C\ {0} defined by g(z) = (2-1)-¹. (d) g: Rx [0, 1] → C defined by g((x, y)) = |x|cis(2ny). (e) g: C → R defined by g(z) = |z|.
Transcribed Image Text:Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it is not. (a) g: C→C defined by g(z) = z² + 1. (b) g: C\ {0} → C defined by g(z) = 2¹. (c) g: C\ {1} → C\ {0} defined by g(z) = (2-1)-¹. (d) g: Rx [0, 1] → C defined by g((x, y)) = |x|cis(2ny). (e) g: C → R defined by g(z) = |z|.
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