Answer
$(-\infty,\frac{1}{4})\cup(2,\infty)$
Work Step by Step
Step 1. The domain requirement for the given function
$f(x)=\frac{1}{\sqrt {4x^2-9x+2}}$
is that
$4x^2-9x+2\gt0$
Step 2. Factor the inequality; we have
$(4x-1)(x-2)\gt0$
and the boundary points are $x=1/4, 2$
Step 3. Using test points to examine signs across the boundary points, we have
$...(+)...(1/4)...(-)...(2)...(+)...$
Thus the solutions are $x\lt\frac{1}{4}$ or $x\gt2$
Step 4. We can express the solutions in interval notation as $(-\infty,\frac{1}{4})\cup(2,\infty)$
