# How do you state the domain and range of f(x)=x^2-2?

Feb 9, 2017

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R}$
The range is y in [-2, +oo[

#### Explanation:

$f \left(x\right)$ is a polynomial function

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R}$

Let $y = {x}^{2} - 2$

${x}^{2} = y + 2$

$x = \sqrt{y + 2}$

So,

${f}^{-} 1 \left(x\right) = \sqrt{x + 2}$

The domain of ${f}^{-} 1 \left(x\right)$ is the range of $f \left(x\right)$

Therefore,

$x + 2 \ge 0$

$x \ge - 2$

The range is y in [-2, +oo[