Question

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

Answer 1

`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 `RR` for positive real values.

Consider that if `|x|> 1` then `1"/"|x| < 1`. So we can say that `ln(1+1"/"x)` will be defined for all `x<-1` and obviously will be defined for all `x>0`.

We also see that `x!=0` since we have `x` in the denominator.

So `D_f=(-oo,-1)∪(0,oo)`