# What is the domain and range of  f(x)=sqrt(5x-10)?

Aug 2, 2018

$x \in \mathbb{R} , x \ge 2$
$y \in \mathbb{R} , y \ge 0$

#### Explanation:

$\text{For the radical we require}$

$5 x - 10 \ge 0 \Rightarrow 5 x \ge 10 \Rightarrow x \ge 2$

$\text{domain is } x \in \mathbb{R} , x \ge 2$

$\left[2 , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

$f \left(2\right) = 0$

$\text{range is } y \in \mathbb{R} , y \ge 0$

$\left[0 , \infty\right) \text{ in interval notation}$
graph{sqrt(5x-10) [-10, 10, -5, 5]}