Answer
$(\frac{1}{2}, 1]$
Work Step by Step
Step 1. The domain requirement for the given function $f(x)=\sqrt {\frac{x}{2x-1}-1}$ is that $\frac{x}{2x-1}-1\geq0$
Step 2. From the above inequality, we have
$\frac{x-2x+1}{2x-1}\geq0$, $\frac{-x+1}{2x-1}\geq0$, and $\frac{x-1}{2x-1}\leq0$; the boundary points are $x=1/2,1$
Step 3. Using test points to examine signs of the left side across the boundary points, we have
$...(+)...(1/2)...(-)...(1)...(+)...$
Thus the solutions are $\frac{1}{2}\lt x\leq 1$
Step 4. We can express the solutions in interval notation as $(\frac{1}{2}, 1]$
