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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 54E
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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.
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
Transcribed Image Text:an [a,b] and an [a, b] → f(an) → f(x) ;antan [a,b] anx ; and
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