How do you find the domain and range of root4(9-x^2)?

Aug 1, 2017

Domain : $- 3 \le x \le 3$ or $\left[- 3 , 3\right]$
Range: $0 \le f \left(x\right) \le \sqrt{3} \mathmr{and} \left[0 , \sqrt{3}\right]$

Explanation:

$f \left(x\right) = \sqrt[4]{9 - {x}^{2}}$ . For domain under root must be $\ge 0$

$\therefore 9 - {x}^{2} \ge 0 \mathmr{and} {x}^{2} \le 9 \therefore x \le 3 \mathmr{and} x \ge - 3$

Domain : $- 3 \le x \le 3$ or $\left[- 3 , 3\right]$

Range : Minimum value : $f \left(x\right) = 0$ when $x = \pm 3$ and

maximum value : $f \left(x\right) = \sqrt{\left(\sqrt{9}\right)} = \sqrt{3}$ when $x = 0$

Range: $0 \le f \left(x\right) \le \sqrt{3} \mathmr{and} \left[0 , \sqrt{3}\right]$

graph{(9-x^2)^0.25 [-10, 10, -5, 5]} [Ans]