Answer:
The equation is defined for y values in the closed interval [tex][-\sqrt{10},\sqrt{10}][/tex].
Step-by-step explanation:
[tex]x^2+y^2-10=0\\\implies x^2 = 10-y^2[/tex]
Since x^2 is a non-negative quantity, this implies the following inequality must hold:
[tex]10-y^2\geq0\\y^2\leq 10\\|y|\leq \sqrt{10}\\\implies -\sqrt{10}\leq y \leq \sqrt{10}[/tex]
In other words, y must lie between [tex]\pm \sqrt{10}[/tex], inclusively.
