Let $f ( x ) = \log _ { \mathrm { e } } x$ and $g ( x ) = \frac { x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 2 x + 2 } { 2 x ^ { 2 } - 2 x + 1 }$. Then the domain of $f \circ g$ is\\
(1) $[ 0 , \infty )$\\
(2) $[ 1 , \infty )$\\
(3) $( 0 , \infty )$\\
(4) $\mathbb { R }$