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Math Help - Piecewise continuous

  1. #1
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    Piecewise continuous

    Let D=[0,1] \cup (2,3] and define f: D \rightarrow \mathbb{R} by  f(x) = \left\{\begin{array}{cc}x,&\mbox{ if }<br />
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  x_0 \in [0,1] , would I pick x \in [0,1] with  |x-x_0| < \delta , then process with the proof, then do the same for (2,3]?
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    Hello,
    Quote Originally Posted by tttcomrader View Post
    Let D=[0,1] \cup (2,3] and define f: D \rightarrow \mathbb{R} by  f(x) = \left\{\begin{array}{cc}x,&\mbox{ if }<br />
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  x_0 \in [0,1] , would I pick x \in [0,1] with  |x-x_0| < \delta , then process with the proof, then do the same for (2,3]?
    Yes, and you'll prove that f is continuous separately on [0,1] and (2,3]
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