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Yes, you did a great job! Those are the exact steps to take.
The answer is 4 +/- sqrt(x) (Note I used x in the answer, not y. But you had the right steps. -- this is why I originally used f(x) and x when solving it. If you're going to use y, don't forget to swap it back out for x at the end.)
The domain here is x >= 0, so that the inside of the square root is >= 0.
Glad to help, have a great evening!