I am trying to find such a function or a proof, which shows that there is no such function in general. I know, that the other direction of this statement is true. (I prooved it using only the definiton). But here I have no idea, how to show it. Thank you
2026-03-29 02:36:15.1774751775
Is there any noncontinuous function f(x), such that the absolute value of f(x) is continuous?
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HINT: Such functions do exist. Can you find one that takes one value on the rational numbers and a different value on the irrational numbers?