11. The range of the function $y=x+\sqrt{x^{2}-3 x+2}$ is $\qquad$
$$
\begin{array}{l}
y=x+\sqrt{x^{2}-3 x+2} \Rightarrow\left\{\begin{array} { l } 
{ y - x = \sqrt { x ^ { 2 } - 3 x + 2 } , } \\
{ y \geqslant x }
\end{array} \Rightarrow \left\{\begin{array}{l}
y^{2}-2 x y+3 x-2=0, \\
y \geqslant x
\end{array}\right.\right. \\
\Rightarrow x=\frac{y^{2}-2}{2 y-3} \leqslant y \Rightarrow \frac{y^{2}-2-2 y^{2}+3 y}{2 y-3} \leqslant 0 \Rightarrow \frac{y^{2}-3 y+2}{2 y-3} \geqslant 0
\end{array}
$$
$\Rightarrow y \in\left[1, \frac{3}{2}\right) \cup[2,+\infty)$. Therefore, the range of the function $y$ is $\left[1, \frac{3}{2}\right) \cup[2,+\infty)$.