5. Consider the permutationsf=on the set {1, 2, 3, 4).(b) T(c) (12342 1 3 4Find fog and go f.Find f, and verify thatFind g, and verify that1gog-¹ = (11 2 3 4and g314 2sos¹ = ( 1 2 3 4) = ² os2 3 4)=g-log2 3 4

Answered: Image /qna-images/answer/e74cb2b7-3c50-422e-aa99-ffb18d9211f3.jpg

Answered: 5. Consider the permutations f 1 2 3 4…

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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7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.
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5. Consider the permutations f 1 2 3 4 2 1 3 4 on the set {1, 2, 3, 4). (a) Find fog and go f. (b) F Find f, and verify that ƒoƒ-¹ = (c) ( Find g¹, and verify that and g= 1 2 3 4 3142 1 2 3 4 1 2 3 4 12 ) = 5¹ of 908¹-(1 2 3 4) = 9¹09 gog-¹ =g¹og