$$y=|2^{x}-2|$$
$\left\{\begin{matrix}x=\log_{2}\left(2-y\right)\text{, }&y\geq 0\text{ and }y<2\\x=\log_{2}\left(y+2\right)\text{, }&y\geq 0\end{matrix}\right.$
$y=|2^{x}-2|$