Answered: Let K> 0 and let f: RR satisfy the…

Let K> 0 and let f: RR satisfy the condition f(x)-f(y)| ≤ Kx-y for all x, y € R. Show that f is continuous at every point e E R.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Let K> 0 and let f: RR satisfy the condition f(x)-f(y)| ≤ Kx-y for all x, y € R.
Show that f is continuous at every point c E R.

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Step 1: Definition of continuity.

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Step 2: Prove that f is continuous at c in R.

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Step 3: Prove that f is continuous at every point c in R.

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