Note: The notation Z refers to the set {0, 1, 2, ..., n − 1}. For example, Z4 = {0, 1, 2, 3}. (a) fZ6Z6 defined by f(x) = x² +4 (mod 6). (b) g: Z5 → Z5 defined by g(x) = x² – 11 (mod 5). - (c) h: ZxZZ defined by h(x, y) = x+2y. - (d) j : R – {3} → R defined by j(x) = 4x x - 3 -

Note: The notation Z refers to the set {0, 1, 2, ..., n − 1}. For example, Z4 = {0, 1, 2, 3}. (a) fZ6Z6 defined by f(x) = x² +4 (mod 6). (b) g: Z5 → Z5 defined by g(x) = x² – 11 (mod 5). - (c) h: ZxZZ defined by h(x, y) = x+2y. - (d) j : R – {3} → R defined by j(x) = 4x x - 3 -

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 30E: 30. Prove statement of Theorem : for all integers .

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Question

Determine whether each function is an injection and determine whether each is a surjection.

Note: The notation Z refers to the set {0, 1, 2, ..., n − 1}. For example, Z4 = {0, 1, 2, 3}.
(a) fZ6Z6 defined by f(x) = x² +4 (mod 6).
(b) g: Z5 → Z5 defined by g(x) = x² – 11 (mod 5).
-
(c) h: ZxZZ defined by h(x, y) = x+2y.
-
(d) j : R – {3} → R defined by j(x) =
4x
x - 3
-

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