Let R* denotes the set of positive real numbers and let f: R+ R+ be the bijection defined by ƒ (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 E R+, find a formula for xy. What is the identity element of (R+, 0)? (b) For x E R+, find a formula for the inverse of x under ».
Let R* denotes the set of positive real numbers and let f: R+ R+ be the bijection defined by ƒ (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 E R+, find a formula for xy. What is the identity element of (R+, 0)? (b) For x E R+, find a formula for the inverse of x under ».
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:R+
I
Let R* denotes the set of positive real numbers and let ƒ: 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 x
of (R+, 0)?
(b) For x = R+, find a formula for the inverse of x under ».
y. What is the identity element
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