If R be the additive group of real numbers and R+the multiplicative group of positive real numbersshow that the following mapping are isomorphism.(i) f: R→ R+ s. t. f(x) = e×, × € R.(ii) f: R+ → R s. t. f(x) = log ×, xe R¹.

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Answered: If R be the additive group of real…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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If R be the additive group of real numbers and R+ the multiplicative group of positive real numbers show that the following mapping are isomorphism_ (i) f: R→ R+ s. t. f(x) = ex, x € R. (ii) f: R+ → Rs. t. f(x) = log x, XER+.