Let d be a metric on X + 0. Show that the function e defined byd(a, b)1+ d(a, b)e(a, b) =%3Dwhere a, b e X, is also a metric on X.

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Answered: Let d be a metric on X + 0. Show that…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 44E

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Let d be a metric on X + 0. Show that the function e defined by d(a, b) 1+ d(a, b) e(a, b) = %3D where a, b e X, is also a metric on X.