Suppose that f is continuous at every point of [a, b] and that f(x) = 0...

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Suppose that f is continuous at every point of [a, b] and that f(x) = 0
whenever x is rational. Prove that f(x) = 0 for all x ∈ [a, b].

math Advanced-Math

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Answer 1

Answer #1

f is continuens at every point of [a,b] and let f(2)=0 whenever n is ratione Let consider to continuens function gon)zotrit. Then by hypothesis. (an [a,b]) e s é [a,b mi since s is closed set by theorem. ) Now, Can [a, b]) cs =) [a b c CS s s = [a,

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