# Domain of a function?

## which of the following intervals are contained in the domain of the function - $\sqrt{2 x - {x}^{3}}$

May 17, 2018

The Domain of a function

$\left(- \infty , - \sqrt{2}\right] \mathmr{and} \left[0 , \sqrt{2}\right]$

#### Explanation:

show below

$y = \sqrt{2 x - {x}^{3}}$

let $2 x - {x}^{3} \ge 0$

$2 x - {x}^{3} = 0$

$x \left(2 - {x}^{2}\right) = 0$

$x = 0$

$2 - {x}^{2} = 0$

${x}^{2} = 2 \Rightarrow x = \pm \sqrt{2}$

The Domain of a function

$\left(- \infty , - \sqrt{2}\right] \mathmr{and} \left[0 , \sqrt{2}\right]$