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Thread: Defining a continuous piecewise function

  1. #1
    Junior Member
    Mar 2017

    Question Defining a continuous piecewise function

    I would really appreciate someone's help on a piecewise function-related question that I have. I'm wondering in the case when a piecewise function is continuous, does it matter which sub-function (in the case when there's two sub-functions) is defined as the less than or equal to sub-function? I would think that it would not matter since they are connected after all, but I just want confirmation for my reasoning is right. I attached an example in this post. Thanks
    Defining a continuous piecewise function-17408029_1342014722521285_922736812_o.jpg
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  2. #2
    MHF Contributor

    Aug 2006

    Re: Defining a continuous piecewise function

    Is it clear to you that these two functions are equivalent?
    $f(x)=\begin{cases}\sqrt{x} &: x\ge 1 \\ |x| &: x<1\end{cases}$ and $g(x)=\begin{cases}\sqrt{x} &: x>1 \\ |x| &: x\le 1\end{cases}$

    If not surely the only question is possibly about $x=1$.
    But $\displaystyle{ f(1) = {\lim _{x \to 1}}f(x) = 1 = g(1) = {\lim _{x \to 1}}g(x) }$ removes all doubt.
    Thanks from topsquark
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