# What is the domain and range of f(x) = ln (10-x)?

Jan 14, 2018

domain: $x < 10$
range: $\mathbb{R}$

#### Explanation:

$\ln \left(x\right)$ graph: graph{ln(x) [-10, 10, -5, 5]}
the natural log function only outputs a real number if the input is greater than 0.

this means the domain is $10 - x > 0$
$x < 10$

the natural log function can output any real number, so the range is all real numbers.

check with this graph
$f \left(x\right) = \ln \left(10 - x\right)$ graph{ln(10-x) [-10, 10, -5, 5]}