Suppose h is continuous on ℝ and h(q) = 0 for every rational number q. Does it follow that h(x) = 0 for all x ∈ ℝ ? Justify your answer!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 52E
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Suppose h is continuous on ℝ and h(q) = 0 for every rational number q. Does it follow that h(x) = 0 for all x ∈ ℝ ? Justify your answer!

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