(b) Let f and g be contraction functions with co (i) The composite function h := fog is also a contraction function: (ii) Using (i) prove that h(x) = cos(sin x) is continuous at every point x = xo; that is, limo | cos(sin x)| = | cos(sin(ão))

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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(b) Let f and g be contraction functions with common domain R. Prove that
(i) The composite function h := fog is also a contraction function:
(ii) Using (i) prove that
h(x) = cos(sin x)
r)| |
is continuous at every point x = ro; that is, lim, cos(sin x) = cos(sin(ro))|.
W
Transcribed Image Text:(b) Let f and g be contraction functions with common domain R. Prove that (i) The composite function h := fog is also a contraction function: (ii) Using (i) prove that h(x) = cos(sin x) r)| | is continuous at every point x = ro; that is, lim, cos(sin x) = cos(sin(ro))|. W
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