Let g : R R satisfy the relation g(x + y) = g(x) g(y) for all

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Let g : R → R satisfy the relation g(x + y) = g(x) g(y) for all x, y in R. Show that if g is continuous at x = 0, then g is continuous at every point of R. Also if we have g(a) = 0 for some a ∈ R, then g(x) = 0 for all x ∈ R.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 10:59 AM

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Let g : R R satisfy the relation g(x + y) = g(x) g(y) for all

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First show that either g0 0 or g0 1 Next if g 0 for some R and if x R let y x so that ...View the full answer

Introduction to Real Analysis

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