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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80f0fd83-d44a-4dc1-b23c-0550049a776e%2F2dfe9ddb-73bb-49ac-bd02-972a7cf76f62%2Flbjf1f8_processed.jpeg&w=3840&q=75)
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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