# How do you find the domain and range of sqrt(8-x)?

Mar 20, 2017

Domain: $\left[8 , - \infty\right)$ , Range: $\left[0 , \infty\right)$

#### Explanation:

$y = \sqrt{8 - x}$ , Domain : $8 - x \ge 0 \therefore 8 \ge x \mathmr{and} x \le 8 \therefore$ Domain: $\left[8 , - \infty\right)$

Range : $y \ge 0 \therefore$ Range : $\left[0 , \infty\right)$ graph{(8-x)^0.5 [-10, 10, -5, 5]} [Ans]

Mar 20, 2017

Domain: $x \le 8 \textcolor{w h i t e}{\text{xxx}}$or $\left(- \infty , 8\right]$
Range: $\left[0 , + \infty\right)$
$\textcolor{w h i t e}{\text{XXXXXXXXX}}$assuming we are restricted to $\mathbb{R}$, the set of real numbers.

#### Explanation:

$\sqrt{8 - x}$ is defined (in $\mathbb{R}$) for all values of $x$ for which $\left(8 - x\right) \ge 0$;
that is for $x \le 8$. [This gives us our "Domain"].

$\sqrt{\text{anything}}$ is defined as the primary root i.e. a value $\ge 0$
At $x = 8$, $\textcolor{w h i t e}{\text{XXXXXXX}} \sqrt{8 - x} = 0$
and as $x \rightarrow - \infty$, $\textcolor{w h i t e}{\text{XX}} \sqrt{8 - x} \rightarrow + \infty$
[This gives us our "Range"].