Respuesta :

LammettHash

Use the definition of absolute value:

[tex]|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}[/tex]

This means for [tex]-2<x<3[/tex], we have

  • [tex]|x-3|=-(x-3)=3-x[/tex] because [tex]x<3[/tex]
  • [tex]|x+2|=x+2[/tex] because [tex]x>-2[/tex]
  • [tex]|x-5|=-(x-5)=5-x[/tex] because [tex]x<5[/tex]

So we end up with

[tex]y=(3-x)+(x+2)-(5-x)\implies y=x[/tex]

over the given interval.