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.

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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.
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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