If f(x)=2-x^1/2 and g(x)+x^2-9, what is the domain of g(x)/f(x)?

As far a domain, you only care about the denominator and radicals.

f(x) = 2 - √x is the denominator, so it can't be 0. 
Also x is under a radical, so x can't be negative.
Set the denominator equal to 0 to find the excluded values.

2 - √x = 0
-√x = -2
√x = 2
x = 4, so 4 is an excluded value

The domain is all real numbers greater than or equal to 0, except 4.
[0, 4) U (4, ∞)
0 ≤ x < 4 U x > 4