48. Let f be a function defined on ]0, 1[ by : 0, if x is irrational f(x) ={1/q, if x=p/q; where p and q are positive integers having no common factor. %3D 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 irrational f(x) ={1/q, if x=p/q; where p and q are positive integers having no common factor. %3D 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%2F167b2585-d12c-48f9-800c-0de8f67e18ee%2Fef8bfbaa-6b0f-46bd-bdde-1a43279f2c76%2Fh3smv5_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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