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

Jun 13, 2018

Domain $\left[- 5 , + \infty\right)$, Range: $\left[0 , + \infty\right)$

#### Explanation:

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

Assuming $f \left(x\right) \in \mathbb{R}$ then $f \left(x\right)$ is defined $\forall x \ge - 5$

Hence, the domain of $f \left(x\right)$ is $\left[- 5 , \infty\right)$

Now consider, $f \left(- 5\right) = 0$ and $f \left(x\right) > 0 \forall x > - 5$

Also, since $f \left(x\right)$ has no finite upper bound.

The range of $f \left(x\right)$ is $\left[0 , + \infty\right)$

We can infer these results from the graph of $f \left(x\right)$ below.

graph{sqrt(x+5) [-10, 10, -5, 5]}