Let X = { n Î Z | 1 £ n £6 } and consider the two functions f : X ® X , g : X ® X , expressed in their graph form as follows: F = { (1,2), (2,4), (3,3), (4,4), (5,1), (6,6) }  G = { (1,2), (2,4), (3,6), (4,2), (5,4), (6,6) } State the following functions in graph form (that is, as a subset of X×X):        g°f, g°g.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.7: Functions Defined By Equations
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Let X = { n Î Z | 1 £ n £6 } and consider the two functions f : X ® X , g : X ® X ,

expressed in their graph form as follows:
F = { (1,2), (2,4), (3,3), (4,4), (5,1), (6,6) }

 G = { (1,2), (2,4), (3,6), (4,2), (5,4), (6,6) }

State the following functions in graph form (that is, as a subset of X×X):       

  1. g°f,
  2. g°g.

Answer:

  • The graph representation of g o f   is 

 

 

  • The graph representation of g o g  is 
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