Define f:R → R by ƒ (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is discontinuous at 1 and continuous at 2. Are there any other points besides 2 at which fis continuous? 2.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.6: Rational Functions
Problem 1E: If the rational function y=r(x) has the vertical asymptote x=2, then as x2+ , either y ______or y...
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Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove
that f is discontinuous at 1 and continuous at 2. Are there any other points besides 2 at
which f is continuous?
2.
Transcribed Image Text:Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is discontinuous at 1 and continuous at 2. Are there any other points besides 2 at which f is continuous? 2.
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