# How do you find the domain of f(x)=sqrt(12 - 2x^2)?

Mar 13, 2018

$\left[- \sqrt{6} , \sqrt{6}\right]$

#### Explanation:

To find the domain of a function, we find all possible values of its input which give a defined function.

Here, we have $\sqrt{12 - 2 {x}^{2}}$

Since when $x < 0$ the function of $\sqrt{x}$ will be undefined, we say this function is defined when:

$12 - 2 {x}^{2} \ge 0$

$6 - {x}^{2} \ge 0$

$- {x}^{2} \ge - 6$

${x}^{2} \le 6$

$- \sqrt{6} \le x \le \sqrt{6}$

So $f \left(x\right)$ is only defined when it is between $- \sqrt{6}$ and $\sqrt{6}$. In interval notation, we write this as:

$\left[- \sqrt{6} , \sqrt{6}\right]$