Let $\space f(x)=\frac{|2-x|+x}{|x|} \space$. How can it be written by pieces?
I've tried to find the zeros of $f$, by solving $f(x)=0$. But it seems that the function don't have real zeros. I stayed without knowing what is the transition point in the piecewise function.
Even without the transition poin, I tried to figure it out the two pieces.
In the original expression, I put the minus signal in evidence, and the expression of $f$ stayed like this:
$\space f(x)=\frac{|-(x-2)|+x}{|x|} \space$
To the right of the transition point would be like this $\frac{-(x-2)+x}{x}=\frac{2}{x} \space$.To the left would be like this $\frac{x-2+x}{-x}=\frac{2x-2}{-x}$.
But the graphs don't seem to be like the original one.
Can you explain me how to write in pieces this function?