# What is the Domain for: h(x)=ln(x+1)?

Apr 11, 2017

$\left(- 1 , + \infty\right)$

#### Explanation:

$h \left(x\right) = \ln \left(x + 1\right)$

$\ln x$ is defined $\forall x > 0$

Hence, $\ln \left(x + 1\right)$ is defined $\forall \left(x + 1\right) > 0 \to x > - 1$

$\therefore$ the domain of $h \left(x\right)$ is $\left(- 1 , + \infty\right)$

This can be seen from the graph of $h \left(x\right)$ below:

graph{ln(x+1) [-11.25, 11.245, -5.62, 5.63]}