1. ## Domain

I'm having a lot of trouble with finding the domain of this question:

$sqrt(8x-4)/sqrt(x)$

I get [.5, inf), which I'm told is wrong.

2. From the denominator it is clear that $x\neq 0$ or $x \neq \mathbb{R}^-$

In the numerator $8x-4 > 0$ giving $x > \frac{1}{2}$

Your solution sounds good to me.