A function f : R -+ JR is said to be additive if f (x + y) = f (x) + f (y) for all x, y in R. Prove that if f is continuous at some point x0 , then it is continuous at every point of R. (See Exercise 4.2.12.)
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Textbook: Introduction to Real Analysis
Author: Robert G. Bartle, Donald R. Sherbert
This full solution covers the following key subjects: . This expansive textbook survival guide covers 48 chapters, and 831 solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. The full step-by-step solution to problem: 12 from chapter: 5.2 was answered by , our top Calculus solution expert on 03/14/18, 07:51PM. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since the solution to 12 from 5.2 chapter was answered, more than 221 students have viewed the full step-by-step answer. The answer to “A function f : R -+ JR is said to be additive if f (x + y) = f (x) + f (y) for all x, y in R. Prove that if f is continuous at some point x0 , then it is continuous at every point of R. (See Exercise 4.2.12.)” is broken down into a number of easy to follow steps, and 52 words.