# What is the domain and range of f(x) = sqrt( x+3)?

Apr 6, 2016

Domain: $x \in \left[- 3 , + \infty\right)$
Range: $f \left(x\right) \in \left[0 , + \infty\right)$

#### Explanation:

Assuming we are limited to Real numbers:

The argument of the square root operation must be $\ge 0$
therefore
$\textcolor{w h i t e}{\text{XXX}} x + 3 \ge 0 \rightarrow x \ge - 3$

The square root operation provides a (primary) value which is non-negative.
As $x \rightarrow + \infty , \sqrt{x + 3} \rightarrow + \infty$
So the range of $f \left(x\right)$ is $0$ to $+ \infty$