Let f be a function defined on ]0, 1I[ by : 0, if x is irrational x= p/q; where p and q are positive f (x) = {1/q, if %3D !! integers having no common factor. Prove that f is continuous at each irrational point and discontinuous at each rational point.
Let f be a function defined on ]0, 1I[ by : 0, if x is irrational x= p/q; where p and q are positive f (x) = {1/q, if %3D !! integers having no common factor. 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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![Let f be a function defined on ]o, 1[ by:
0, if x is irrational
f (x) = {1/g, if x= p/q; wherep 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%2F4fbf087c-b36a-4620-8b1d-cdffae49ede0%2F5c3ba848-4550-40da-95bd-daac4669163e%2Fzew3jbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f be a function defined on ]o, 1[ by:
0, if x is irrational
f (x) = {1/g, if x= p/q; wherep 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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