4. (a) Let a : Z→ Z be the function defined by a(n) = 2n + 1, and let i: Z → Z be the identity function. Is there a function b: Z→ Z such that bo a = i? Is there a function b: Z → Z such that ao b = i? (b) Let f: N→ N and g: N→ N be defined by f(n) = n + 1, g(n) = Find the functions fog, gof, fogof and go fog. n 1 1 if n > 1 if n = 1.
4. (a) Let a : Z→ Z be the function defined by a(n) = 2n + 1, and let i: Z → Z be the identity function. Is there a function b: Z→ Z such that bo a = i? Is there a function b: Z → Z such that ao b = i? (b) Let f: N→ N and g: N→ N be defined by f(n) = n + 1, g(n) = Find the functions fog, gof, fogof and go fog. n 1 1 if n > 1 if n = 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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Transcribed Image Text:4.
(a) Let a Z→→ Z be the function defined by a(n) = 2n + 1, and let i: Z→ Z be the identity
function.
Is there a function b: Z→ Z such that bo a = i?
Is there a function b: Z→ Z such that a ob=i?
(b) Let f: N N and g: N→ N be defined by
f(n) = n + 1,
n-1
g(n) =
1
Find the functions fog, gof, fogof and gofog.
if n > 1
if n = 1.
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