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Let A = R-{0,1}, the real numbers without 0 and 1, and S+ (ff2f z•f 4f 5•f &} %3D where these are functions from A to A defined by f,(x) =x, f,) (x) = - x- 1 f3(x) =1-x, f,(x) = f(x) = , and f (x) x-1 1-x Given that S under composition of functions is a group. Show that this is not an Abelian group.

Let A = R-{0,1}, the real numbers without 0 and 1, and S+ (ff2f z•f 4f 5•f &} %3D where these are functions from A to A defined by f,(x) =x, f,) (x) = - x- 1 f3(x) =1-x, f,(x) = f(x) = , and f (x) x-1 1-x Given that S under composition of functions is a group. Show that this is not an Abelian group.

Advanced Engineering Mathematics
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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Abstract Algebra 1
QUESTION 11 Let A = R-(0, 1}, the real numbers without 0 and 1, and S+ (f,ff3f f 5-f 6} where these are functions from A to A def ined by f , (x) =x, f) (x) = -, x-1 f3(x) =1-x, f,(x) = f,(x) : = and f „(x) =: 6. x-1 1-x Given that S under composition of functions is a group. Show that this is not an Abelian group.
Transcribed Image Text:QUESTION 11 Let A = R-(0, 1}, the real numbers without 0 and 1, and S+ (f,ff3f f 5-f 6} where these are functions from A to A def ined by f , (x) =x, f) (x) = -, x-1 f3(x) =1-x, f,(x) = f,(x) : = and f „(x) =: 6. x-1 1-x Given that S under composition of functions is a group. Show that this is not an Abelian group.
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