I would plug numbers into y then solve for x to find the domain

As for,

I would clear the radical from said equation entirely by squaring both sides. Then, I would start plugging numbers into and solve for x. You have to be careful though, and then check your results in the origional equation for any extraneous solutions. Give it a shot. Start with -2 on up to 2 and see what happens. Remember to check your solutions.