what is the domain and range of sqrt(81-x^2)?

what is the domain and range of $$\sqrt{81-x^2}$$

    $$\\81-x^2\ge0\\ 81\ge x^2\\ x^2 \le 81\\ -9\le x \le 9 \qquad \mbox{The the domain is [-9,9]} \\$$

The square root of anything is greater or equal to 0  therefore  range does not include less than 0.

$$\sqrt{81-x^2} = \sqrt{81-positive\; number} \;\le \sqrt{81}\le9$$

$$Therefore the range is [0,9]$$

If we exclude complex numbers then the domain is -9 ≤ x ≤ 9 and the range is 0 to 9.  If x lies outside this range then we are looking at the square root of a negative number.

whats the domain and range root of 81-x^2 using u for the union of sets  and inf