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.
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.
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 work out this proof. 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%2F685e1d6f-6085-4c5f-96c2-6744d855aa0c%2Fsfilgur_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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