Q9For each nonzero rational number in the interval (0, 1), write x as p/q where p, q are integers with no commonfactors and p, q> 0, and then define f(x) = 1. Also define f(x) = 0 for all æ € (0, 1) \ Q. Show ƒ is continuousat each point of (0, 1) \ Q and discontinuous at each point of (0, 1) nQ.

For each nonzero rational number in the interval (0, 1), write a as p/q where p, q are integers with no common factors and p, q> 0, and then define f(x) = . Also define f(x) = 0 for all x = (0, 1) \ Q. Show f is continuous at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) Q

For each nonzero rational number in the interval (0, 1), write a as p/q where p, q are integers with no common factors and p, q> 0, and then define f(x) = . Also define f(x) = 0 for all x = (0, 1) \ Q. Show f is continuous at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) Q

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 14T

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Question

Q9
For each nonzero rational number in the interval (0, 1), write x as p/q where p, q are integers with no common
factors and p, q> 0, and then define f(x) = 1. Also define f(x) = 0 for all æ € (0, 1) \ Q. Show ƒ is continuous
at each point of (0, 1) \ Q and discontinuous at each point of (0, 1) nQ.

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