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

Dec 3, 2017

D_f=(-oo,-1)∪(0,oo)

#### Explanation:

The domain of a function is the maximal interval over which it's defined.

The $\ln$ function is defined over $\mathbb{R}$ for positive real values.

Consider that if $| x | > 1$ then $1 \text{/} | x | < 1$. So we can say that $\ln \left(1 + 1 \text{/} x\right)$ will be defined for all $x < - 1$ and obviously will be defined for all $x > 0$.

We also see that $x \ne 0$ since we have $x$ in the denominator.

So D_f=(-oo,-1)∪(0,oo)