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fresh_42

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No. E.g. take ##f(x) = \begin{cases} 1 & \text{ if } x= 0\\ 0 & \text{ if } x\neq 0 \end{cases}##. It's defined for all real numbers, so its domain is ##\mathbb{R}## whereas it is not continuous at ##x=0##. Of course you can easily find more complicated examples.

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