3. Suppose ƒ is continuous on [0, ∞) and ƒ is uniformly continuous on [1, ∞). Provethat ƒ is uniformly continuous on [0, ∞).4. Suppose f is defined on R and f satisfies|ƒ(x) − f (y)| ≤ C\x − y|ªfor all x, y € R. Here C and a are two given positive constants. Prove that f is uniformlycontinuous on R.

Answered: Image /qna-images/answer/7709aaf1-f744-43b2-a203-877ee9cb916c.jpg

3. Suppose f is continuous on [0, ∞) and ƒ is uniformly continuous on [1, ∞). Prove that f is uniformly continuous on [0, ∞). 4. Suppose f is defined on R and f satisfies |f(x) = f(y)| ≤ C\x − ya for all x, y E R. Here C and a are two given positive constants. Prove that f is uniformly continuous on R.

3. Suppose f is continuous on [0, ∞) and ƒ is uniformly continuous on [1, ∞). Prove that f is uniformly continuous on [0, ∞). 4. Suppose f is defined on R and f satisfies |f(x) = f(y)| ≤ C\x − ya for all x, y E R. Here C and a are two given positive constants. Prove that f is uniformly continuous on R.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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Question

3. Suppose ƒ is continuous on [0, ∞) and ƒ is uniformly continuous on [1, ∞). Prove
that ƒ is uniformly continuous on [0, ∞).
4. Suppose f is defined on R and f satisfies
|ƒ(x) − f (y)| ≤ C\x − y|ª
for all x, y € R. Here C and a are two given positive constants. Prove that f is uniformly
continuous on R.

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