Answer
$\{x|x\lt1\ or\ x\gt2 \}$.
Work Step by Step
The domain requirement for this function is $x^2-3x+2\gt0 \Longrightarrow (x-1)(x-2)\gt0$ with boundary points $x=1,2$. The "$\gt$" sign indicates that the solution will be outside the region between the boundary points, thus we have $\{x|x\lt1\ or\ x\gt2 \}$.