# What is the domain and range of y(x)=ln(x+2)?

May 21, 2018

The domain is $x \in \left(- 2 , + \infty\right)$.
The range is $y \in \mathbb{R}$

#### Explanation:

What's in the log function is $> 0$

Therefore,

$x + 2 > 0$

$x > - 2$

The domain is $x \in \left(- 2 , + \infty\right)$

Let $y = \ln \left(x + 2\right)$

$x + 2 = {e}^{y}$

$x = {e}^{y} - 2$

$\forall y \in \mathbb{R} , {e}^{y} > 0$

The range is $y \in \mathbb{R}$

graph{ln(x+2) [-8.54, 23.5, -9.32, 6.7]}