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For the function: $$f(x) = \begin{cases}0 & ~~\text {if}~~ x=-1;\\ -x & ~~\text{if}~~ -1 \lt x \lt 0;\\ x & ~~\text{if } 0 \le x\le 1 \end{cases}$$ $$f(x+2) = f(x) + 1$$ make this graph, and watch the graph.

I'm sure that $y=f(x)$ is discontinuous at $x=1$, but about $x \in [0,1]$, $x$ is continuous at $x=1$ ?

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    Do you mean that $f(x)$ is discontinuous at $x=-1$. So, what's the question.2012-02-17
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    I tend to believe this kind of questions are spam.2012-02-17
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    @Kannappan, I'd guess the question is, "Is $f(x)$ continuous at $x=1$?"2012-02-17
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    @RahulNarain Isn't that a kind of obvious, if you know that continuity at end points is determined by one sided limits?2012-02-17
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    Have you drawn the graph? It is a rising sequence of disconnected V shapes.2012-02-17

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