(5) Let f : Z→Z be a mapping defined by { т if m is even, f(m) = 2m + 1 if m is odd. (a) Verify that f is one-to-one. (b) Since f is one-to-one, find an inverse g : Z → Z such that gof = id.
(5) Let f : Z→Z be a mapping defined by { т if m is even, f(m) = 2m + 1 if m is odd. (a) Verify that f is one-to-one. (b) Since f is one-to-one, find an inverse g : Z → Z such that gof = id.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(5)
Let f : Z→ Z be a mapping defined by
m
if m is even,
f(m) =
2m + 1
if m is odd.
(a) Verify that f is one-to-one.
(b) Since f is one-to-one, find an inverse g : Z→ Z such that gof = id.
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