# analysis – express \$f\$ in the interval \$[0, 2]\$

In a question of an exercise, I have to “express the following function in the interval $$(0, 2)$$ ” :

$$fleft(xright)=left|x-2leftlfloorfrac{x+1}{2}rightrfloorright|$$

My initial idea would be that I have to express the function without the absolute value…

Therefore, I tried working with inequalities, starting with
$$0 le x le 2$$ and $$-x-1le :2lfloor frac{x+1}{2}rfloor < -x+1$$ to get some significant result (i.e: the function is always positive or negative), however I didn’t get to anything meaningful when summing the two inequalities, and, by seeing the plot of $$f$$ without the absolute value, it is both positive and negative in this interval.

What am I supposed to do? Did I understand the question wrong?