# What is the domain and range of f(x) = ln(x): x>0?

Sep 26, 2016

$\left(- \infty , + \infty\right)$

#### Explanation:

$f \left(x\right) = \ln x$ is, as you state, defined for $x > 0$. Thus its domain is 0,+oo).

On the other hand, since ${\lim}_{\text{x->0}} \ln x = - \infty$ the range of $\ln x$ is $\left(- \infty , + \infty\right)$

We can get a sense of this by looking at the graph of $\ln x$ below:

graph{lnx [-1.596, 9.504, -3.33, 2.217]}