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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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 25E
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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/n for m 0. h(0) = 0 Here m and 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.
Transcribed Image Text: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/n for m 0. h(0) = 0 Here m and 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.
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