# What is the domain and range of ln(x - 3) + 2?

Jun 19, 2016

Domain is $\left(3 , + \infty\right)$ and range is $\mathbb{R}$

#### Explanation:

The domain is obtained by solving

$x - 3 > 0$

$x > 3$

Let be $y = \ln \left(x - 3\right) + 2$

$\ln \left(x - 3\right) = y - 2$

$x - 3 = {e}^{y - 2}$

$x = {e}^{y - 2} + 3$

that is calculated for all y

so the range of y is $\mathbb{R}$