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Let R+ denotes the set of positive real numbers and let ƒ : R+ →→→ R+ be the bijection defined by f(x) = = 3x, for x > 0. Let denote the ordinary real number multiplication and let be the binary operation on R+ such that ƒ : (R+, ·) → (R+, ) is a group isomorphism. . (a) If x, y € R+, find a formula for xy. What is the identity element of (R+,)? (b) For x € R+, find a formula for the inverse of x under .

Let R+ denotes the set of positive real numbers and let ƒ : R+ →→→ R+ be the bijection defined by f(x) = = 3x, for x > 0. Let denote the ordinary real number multiplication and let be the binary operation on R+ such that ƒ : (R+, ·) → (R+, ) is a group isomorphism. . (a) If x, y € R+, find a formula for xy. What is the identity element of (R+,)? (b) For x € R+, find a formula for the inverse of x under .

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 R+ denotes the set of positive real numbers and let f: R+ →→ R+ be the bijection defined by f(x) = 3x, for x > 0. Let denote the ordinary real number multiplication and let be the binary operation on R+ such that ƒ : (R+, .) → (R+, ) is a group isomorphism. . (a) If x, y € R+, find a formula for xy. What is the identity element of (R+, 0)? (b) For x € R+, find a formula for the inverse of x under .
Transcribed Image Text:Let R+ denotes the set of positive real numbers and let f: R+ →→ R+ be the bijection defined by f(x) = 3x, for x > 0. Let denote the ordinary real number multiplication and let be the binary operation on R+ such that ƒ : (R+, .) → (R+, ) is a group isomorphism. . (a) If x, y € R+, find a formula for xy. What is the identity element of (R+, 0)? (b) For x € R+, find a formula for the inverse of x under .
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