# What is the domain and range of f(x) = ln(-x + 5) + 8?

Apr 29, 2018

The domain is $x \in \left(- \infty , 5\right)$. The range is $y \in \left(- \infty , + \infty\right)$

#### Explanation:

Let $y = \ln \left(- x + 5\right) + 8$

For the natural log,

$- x + 5 > 0$

Therefore,

$x < 5$

The domain is $x \in \left(- \infty , 5\right)$

${\lim}_{x \to - \infty} y = + \infty$

${\lim}_{x \to 5} y = - \infty$

The range is $y \in \left(- \infty , + \infty\right)$

graph{ln(5-x)+8 [-47.05, 17.92, -10.28, 22.2]}