4. Recall S(R) is the group of all permutation ofR under the composition of functions. For any pair of real mumbers a0 and b, define a function fa:R-Ras follows fas (x) = ax +b a. Prove that fa e S(R). That is fan is a permutation of R. h. fan fea facad o, where fas fea is the composition of fan and fet . Vas )"- where (fa )" is the inverse of fa d. Let H= (fa ja eR bERa 0). Prove that Hisa subgroup of S(R).
4. Recall S(R) is the group of all permutation ofR under the composition of functions. For any pair of real mumbers a0 and b, define a function fa:R-Ras follows fas (x) = ax +b a. Prove that fa e S(R). That is fan is a permutation of R. h. fan fea facad o, where fas fea is the composition of fan and fet . Vas )"- where (fa )" is the inverse of fa d. Let H= (fa ja eR bERa 0). Prove that Hisa subgroup of S(R).
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:4. Recall S(R) is the group of all permutation of R under the composition of functions. For any
pair of real mumbers a = 0 and b, define a function faa: R-Ras follows
fas (x) = ax +b
a. Prove that fas E S(R). That is faa is a permutation of R.
b. fan o fea = facad , where fas o fea is the composition of fan and fet
(fas )-1 where (fa )* is the inverse of fa
a. Let H= (fa ja e RDERa 0). Prove that H is a subgroup of S(R).
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