Suppose that f : R ---+ (0,00) satisfies f(x + y) = f(x)f(y). Modifying the outline in

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Suppose that f : R ---+ (0,00) satisfies f(x + y) = f(x)f(y). Modifying the outline in Exercise 8, show that if f is continuous at 0, then there is an a E (0,00)

such that f(x) = aX for all x E R. [Note: You may assume that the function aX is continuous on R.]

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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Suppose that f : R ---+ (0,00) satisfies f(x + y) = f(x)f(y). Modifying the outline in

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An Introduction To Analysis

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