# Math Help - absolute value to piecewise

1. ## 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?

2. ## Re: 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?
$\left| {x - 4} \right| = \left\{ \begin{gathered} - x + 4,\;x < 4 \hfill \\ x - 4,\;4 \leqslant x \hfill \\ \end{gathered} \right.$