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.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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%2Fffa9b535-5adb-420d-bef1-68454bca6dd6%2F6d7bdb49-dc28-429f-ad1f-148e748569b4%2Fzn6ve5_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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