# How do you find the domain and range of f(x)=sqrt (x+7)/(x^2+7)?

Dec 25, 2017

domain$\mathbb{R} = \left\{x : x \in \mathbb{R} , x \ge \left(- 7\right)\right\}$and range$\mathbb{R} = \left\{y : y \in \mathbb{R} , y \ge 0\right\}$

#### Explanation:

Suppose,y=$f \left(x\right) = \frac{\sqrt{x + 7}}{{x}^{2} + 7}$
If $x < \left(- 7\right) ,$the mentioned equation can not be definable.

$\frac{\sqrt{x + 7}}{{x}^{2} + 7}$=indefinable,when $x < \left(- 7.\right)$$\textcolor{b r o w n}{\left[A s . \sqrt{- x \in \mathbb{R}} = \left(I N D E F I N A B L E\right)\right]}$

Hence,DomainRR=color(red){{x:x inRR,x>=(-7)}

For the value of domain set,range of the equation will be greater than or equal $0$

*So,RangeRR=color(blue){{y:y inRR,y>=0} *