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Let G be the interval (-1/2, ∞). Let a be the operation on G such that, for all x, y = G, x x y = 4xy + 2(x+y) + 1/2. i. Write down the identity element e for (G, ¤). You need not write a proof of the identity la ii. Prove the inverse law for (G, ¤).

Let G be the interval (-1/2, ∞). Let a be the operation on G such that, for all x, y = G, x x y = 4xy + 2(x+y) + 1/2. i. Write down the identity element e for (G, ¤). You need not write a proof of the identity la ii. Prove the inverse law for (G, ¤).

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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Let G be the interval (-1/2, ∞). Leta be the operation on G such that, for all x, y = G, xxy=4xy + 2(x+y)+ 1/2. i. Write down the identity element e for (G, ¤). You need not write a proof of the identity law. ii. Prove the inverse law for (G, ¤).
Transcribed Image Text:Let G be the interval (-1/2, ∞). Leta be the operation on G such that, for all x, y = G, xxy=4xy + 2(x+y)+ 1/2. i. Write down the identity element e for (G, ¤). You need not write a proof of the identity law. ii. Prove the inverse law for (G, ¤).
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