c) Consider a function f defined on the real numbers as { 0ifais irrational. S(r) = 1/n ifr= m/n with m, n in lowest terms. Show that f is continuous at all irrational numbers.

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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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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c) Consider a function f defined on the real numbers as
{
0ifr is irrational.
1/n if r m/n with m, n in lowest terms.
S(r) =
%3D
Show that f is continuous at all irrational numbers.
Transcribed Image Text:c) Consider a function f defined on the real numbers as { 0ifr is irrational. 1/n if r m/n with m, n in lowest terms. S(r) = %3D Show that f is continuous at all irrational numbers.
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