Because there is a square root, we see that x^2 can be no greater than 9. (or else there will be an imaginary number, which is not allowed in functions) So, we can "unsquare" (not square root, there is a difference) 9 and get x=-3 and 3. Therefore, the domain is -3<=x<=3, which is [-3, 3] in interval notation.
We can take the domain to help us find the range. We see that the greatest number x^2 can be is 9, so we solve for sqrt(9-9)+4. That is 4. We see that the smallest number x^2 can be is 0. Plug that in, and we get 7. Therefore, the range is [4, 7].