Question

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

Answer 1

`(-oo,+oo)`

Explanation:

`f(x) = lnx` is, as you state, defined for `x>0`. Thus its domain is `0,+oo)`.

On the other hand, since `lim_"x->0"lnx =-oo` the range of `lnx` is `(-oo,+oo)`

We can get a sense of this by looking at the graph of `lnx` below:

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