# What is the domain and range of g(x) =ln( 4 - x )?

Jun 9, 2018

Domain: $\left\{x | x \in \mathbb{R} : x < 4\right\}$

Range: $\left\{g \left(x\right) | g \left(x\right) \in \mathbb{R}\right\}$

#### Explanation:

Input to the natural logarithm must be positive so to find the domain:

$4 - x > 0$

$x < 4$

$\left\{x | x \in \mathbb{R} : x < 4\right\}$

For the range look at the end behavior, logarithm are continuous:

$x \to - \infty , g \left(x\right) \to \infty$

$x \to 4 , g \left(x\right) \to - \infty$

$\left\{g \left(x\right) | g \left(x\right) \in \mathbb{R}\right\}$

graph{ln(4-x) [-8.96, 11.04, -6.72, 3.28]}