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**tttcomrader** Let $\displaystyle D=[0,1] \cup (2,3] $ and define $\displaystyle f: D \rightarrow \mathbb{R} $ by $\displaystyle f(x) = \left\{\begin{array}{cc}x,&\mbox{ if }

1 \leq x\leq 0\\x-1, & \mbox{ if } 2<x\leq 3\end{array}\right. $

Prove that f is continuous.

The problem is the disconnected domain, if I pick any point $\displaystyle x_0 \in [0,1] $, would I pick $\displaystyle x \in [0,1] $ with $\displaystyle |x-x_0| < \delta $, then process with the proof, then do the same for (2,3]?