The function h: Z12 → Z18 is defined the formula h([a]) = [3a - 5]. (a) Verify that the function h is well-defined, that is, show that if a, b € Z are such that [a] = [b] in Z12 then [3a - 5] = [3b - 5] in Z18.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 58E
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The function h: Z12 → Z18 is defined by the formula h([a]) = [3a — 5].
(a) Verify that the function h is well-defined, that is, show that if a, b € Z are such that [a] = [b]
in Z12 then [3a - 5] = [3b – 5] in Z18.
Transcribed Image Text:The function h: Z12 → Z18 is defined by the formula h([a]) = [3a — 5]. (a) Verify that the function h is well-defined, that is, show that if a, b € Z are such that [a] = [b] in Z12 then [3a - 5] = [3b – 5] in Z18.
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