# Domain of f(x)=ln((x+1))/x ?

Dec 4, 2017

$\left\{x \in \mathbb{R} : - 1 \le x , x \ne 0\right\}$

#### Explanation:

$x$ is restricted in $\ln \left(x + 1\right)$. Since $\ln \left(x\right)$ is only defined for $x \ge 0$

$x + 1 \ge 0$

But for the denominator $x > 0$ and $x < 0$

So domain is:

$\left\{x \in \mathbb{R} : - 1 \le x , x \ne 0\right\}$