## mathmath333 one year ago Find the least value of $$y$$ if

1. mathmath333

\large \color{black}{\begin{align} y=\text{max}(x-1,3-x)\hspace{.33em}\\~\\ \end{align}}

2. ikram002p

x is real ??

3. mathmath333

x,y $$\in$$ R

4. ikram002p

x<2 then max 3-x x>2 then max x-1 x=2 then y=1

5. IrishBoy123

|dw:1434230429282:dw|

6. xapproachesinfinity

@ikram002p how did you know you need to set x<2 or x>2?

7. ikram002p

Well trying :) I used number line and checked points

8. xapproachesinfinity

i still don't get number for what? what irish did seems good to me was that your line of thinking too?

9. ybarrap

|dw:1434255811951:dw|

10. anonymous

$y=\frac{|x-1+3-x|+|x-1-(3-x)|}{2}=\frac{2+|2x-4|}{2}=1+|x-2|$then $$\min_{y}=1$$