# How do you find the domain and range of sqrt(x+5)?

May 18, 2017

Domain$: \left\{x \in \mathbb{R} | x \ge q - 5\right\}$

Range$: \left\{f \left(x\right) \in \mathbb{R} | f \left(x\right) \ge q 0\right\}$

#### Explanation:

We have: $f \left(x\right) = \sqrt{x + 5}$

The domain of any square root function is dependent on its argument.

The argument must be greater than or equal to zero:

$R i g h t a r r o w x + 5 \ge q 0$

$R i g h t a r r o w x \ge q - 5$

The square root function never produces a negative result.

So the range will be greater than or equal to zero as well:

$R i g h t a r r o w f \left(x\right) \ge q 0$

Therefore, for the function $f \left(x\right) = \sqrt{x + 5}$, the domain is $\left\{x \in \mathbb{R} | x \ge q - 5\right\}$ and the range is $\left\{f \left(x\right) \in \mathbb{R} | f \left(x\right) \ge q 0\right\}$.