1. Let f, g, and h be defined on [0, 1] :f(x) = g(x) = h(x) = 0whenever x is irrational;f(x) = 1 and g(x) = xwhenever x is rational;h(x) = 1/n, if x is the rational number x = m/n for m 0.h(0) = 0Here mand n are relatively prime. [m] is the absolute value of m.m € Z - {0}, and n € N.At what points are f, g, and h continuous? Justify your answer.

Given: f,g, h be defined on [0,1] as fx=1 x∈ℚ0 x∈ℚc gx=x x∈ℚ0 x∈ℚchx=1/n x=mn∈ℚ…

1. Let f, g, and h be defined on [0, 1]: f(x) = g(x) = h(x) = 0 whenever x is irrational; f(x) = 1 and g(x) = = X whenever x is rational; h(x) = 1/n, if x is the rational number x = m m/n for m 0. h(0) = 0 Here m and n are relatively prime. [m] is the absolute value of m. me Z-{0}, and n E N. At what points are f, g, and h continuous ? Justify your answer.

1. Let f, g, and h be defined on [0, 1]: f(x) = g(x) = h(x) = 0 whenever x is irrational; f(x) = 1 and g(x) = = X whenever x is rational; h(x) = 1/n, if x is the rational number x = m m/n for m 0. h(0) = 0 Here m and n are relatively prime. [m] is the absolute value of m. me Z-{0}, and n E N. At what points are f, g, and h continuous ? Justify your answer.

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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