Trouble with a domain problem

Hi, I'm having trouble with a domain problem, I think I'm going about it the wrong way, or maybe I'm missing something.

$\displaystyle f(x) = \sqrt{2x+2}$

$\displaystyle g(x) = (x-5)/x$

$\displaystyle (f o g)(x) = ?$

I need to find the domain of (f o g)(x). I started by finding (f o g)(x). I got:

$\displaystyle (f o g)(x) = \sqrt{(4x-10)/x}$

I've found that f(x) must be greater than -1 and g(x) cannot equal 0. So the ranges so far would be:

[-1, 0)U(0,inf)

Then I looked at the limitations of (f o g)(x). I found that it x cannot equal 0, x must be greater than or equal to $\displaystyle \frac{5}{2}$. So as I see it, the limits I listed for f(x) and g(x) can be disregarded, since x must be greater than 2.5, which is bigger than -1 or 0.

My final answer should be:

[$\displaystyle \frac{5}{2}$,inf)

Or so I thought, I tried to submit that answer and it came back as incorrect.

Am I solving this the wrong way? Thanks in advance.