(a) Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show f is discontinuous at every x in R. (b) Let h(x)=x for rational numbers x and h(x) = 0 for irrational numbers. Show h is continuous at x = 0 and at no other point.

(a) Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show f is discontinuous at every x in R. (b) Let h(x)=x for rational numbers x and h(x) = 0 for irrational numbers. Show h is continuous at x = 0 and at no other 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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Question

(a) Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational
numbers. Show f is discontinuous at every x in R.
(b) Let h(x)=x for rational numbers x and h(x) = 0 for irrational
numbers. Show h is continuous at x = 0 and at no other point.

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