to avoid this confusion-you can just invert the completed square in part 11i) to get -->
1. 2(x-2)^2 +3 (completed square form)
2. x, -2 , ^2 , multiply by 2 , +3 (what the x value ungergoes in completed square form)
3.Inverse= x-3 divided by 2, then square root and finally add 2.
4. you will see that the domain has to be x>(or equal) 3
5.and from this you can deduce that the Range(y values) have to be >(or equal to) 2
to be honest im not really answering your question but this is just an alternative..