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Math Help - absolute value to piecewise

  1. #1
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    absolute value to piecewise

    How would you write f(x)=3x-abs(x-4)+1 as piecewise?

    I know we have

    3x-x+4+1=2x+5

    and

    3x+x-4+1=4x-3

    as the two pieces, but how do I the domain for each?
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  2. #2
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    Re: absolute value to piecewise

    Quote Originally Posted by twittytwitter View Post
    How would you write f(x)=3x-abs(x-4)+1 as piecewise?

    I know we have

    3x-x+4+1=2x+5

    and

    3x+x-4+1=4x-3

    as the two pieces, but how do I the domain for each?
    \left| {x - 4} \right| = \left\{ \begin{gathered}   - x + 4,\;x < 4 \hfill \\  x - 4,\;4 \leqslant x \hfill \\ \end{gathered}  \right.
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