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. %3D %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 irrațional f (x) ={1/q, if x=p/q; where p and q are positive integers having no common factor. %3D %3D Prove that f is continuous at each irrational point and discontinuous at each rational point.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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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%2Fe8d7d617-b8c1-467f-af7d-35ae6af3e84b%2F2fb154a3-f614-4c38-a600-95e06d67b7c8%2Fjvgj81e_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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