Answer
$(-\infty,\frac{1}{2}]\cup[2,\infty)$
Work Step by Step
Step 1. The domain requirement for the given function $f(x)=\sqrt {2x^2-5x+2}$ is that $2x^2-5x+2\geq0$
Step 2. Factor the inequality; we have
$(2x-1)(x-2)\geq0$
and the boundary points are
$x=1/2, 2$
Step 3. Using test points to examine signs across the boundary points, we have
$...(+)...(1/2)...(-)...(2)...(+)...$
Thus the solutions are
$x\leq\frac{1}{2}$ or $x\geq2$
Step 4. We can express the solutions in interval notation as $(-\infty,\frac{1}{2}]\cup[2,\infty)$
