Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number in the interval [a, b]. Show that the function f is identically equal to 0.
Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number in the interval [a, b]. Show that the function f is identically equal to 0.
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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Please prove this problem. Thank you
![Exercise 5.3.9.
Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number x in the
interval [a, b]. Show that the function f is identically equal to 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff12a5893-6ffe-4c09-825d-e62643fd26aa%2F626537d6-3290-40ef-a73f-30e40d224696%2Fw0b972l_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 5.3.9.
Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number x in the
interval [a, b]. Show that the function f is identically equal to 0.
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Can I have this notation explained/rewritten
![an [a,b]
and an [a, b] → f(an) → f(x) ;antan [a,b]
anx ; and](https://content.bartleby.com/qna-images/question/f12a5893-6ffe-4c09-825d-e62643fd26aa/c3ce88a6-4a5b-46db-8e0f-4dcd878407f5/m2xfcjf_thumbnail.png)
Transcribed Image Text:an [a,b]
and an [a, b] → f(an) → f(x) ;antan [a,b]
anx ; and
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