Let S ={z=x+i y:|z-1+i| ≥|z|,|z|<2,|z+i|=|z-1|}. Then the set of all values of x, for which w=2 x+ i y ∈ S for some y ∈ R, is

Let $\displaystyle \mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=|z-1|\}$. Then the set of all values of $\displaystyle x$, for which $\displaystyle w=2 x+\mathrm{i} y \in \mathrm{~S}$ for some $\displaystyle y \in \mathbb{R}$, is