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