What is the domain and range of this relation in?

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From: Triamudom Add.math sheet pg.19

work

This is the progress I’ve done so far. As you can see I couldn’t find a way to arrange $x$ in terms of $y $ or vice versa which is required to solve for the domain and range.

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if you work on it $$y=\dfrac{x\pm\sqrt{192-3x^2}}{2}$$ then you will get$$(x,y)\le 8$$ Now,you decide.