# How do you find the domain and range of sqrt1-sqrtx+7 ?

Jun 30, 2017

Domain: $x \ge 0$. In interval notation : $\left[0 , \infty\right)$
Range: $y \le 8$ In interval notation : $\left(- \infty , 8\right]$

#### Explanation:

$y = \sqrt{1} - \sqrt{x} + 7 \mathmr{and} y = 8 - \sqrt{x}$

Domain: Under root should be $\ge 0 \therefore x \ge 0$ ,

Domain: $x \ge 0$. In interval notation : $\left[0 , \infty\right)$

Range: Max $y = 8$ , Minimum: $y = - \infty$

Range: $y \le 8$ In interval notation : $\left(- \infty , 8\right]$

graph{8-x^0.5 [-160, 160, -80, 80]}