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
Related questions
Question
Do.All.Case
![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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
