48. Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p and q are positive integers having no common factor. Prove that f is continuous at each irrational point and discontinuous at each rational point.
48. Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p and q are positive integers having no common factor. Prove that f is continuous at each irrational point and discontinuous at each rational point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![48. Let f be a function defined on ]0, 1[ by :
0, if x is irrational
f (x) = {1/g, if x=p/q; where p and q are positive
integers having no common factor.
Prove that f is continuous at each irrational point and discontinuous
at each rational point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fb99485-6069-44dc-9784-6c28ee85f729%2F311c98fd-de08-4d20-81c0-9a39fb1af539%2Fqycz9qs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:48. Let f be a function defined on ]0, 1[ by :
0, if x is irrational
f (x) = {1/g, if x=p/q; where p and q are positive
integers having no common factor.
Prove that f is continuous at each irrational point and discontinuous
at each rational point.
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