I do not know an example. But I will ask questions if in doubt of the example that you all may provide. Thank you!
Give an example of two functions, both discontinuous at zero, whose product is continuous at zero.
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real-analysis
functions
continuity
1 Answers
3
HINT: There are very simple functions $f(x)$ and $g(x)$ such that $f(x)$ and $g(x)$ are continuous everywhere except at $x=0$, and $f(x)g(x)=0$ for all $x\in\Bbb R$, so that $fg$ is continuous everywhere. You can choose $f(x)$ and $g(x)$ so that each of these functions takes on only the values $0$ and $1$.