# Math Help - Piecewise continuous

1. ## 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 }
1 \leq x\leq 0\\x-1, & \mbox{ if } 2

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]?

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