Question

For what values of `x` is the function `f(x)=ln((x-1)/(x+2))` continuous?

Answer 1

`(-oo,-2) uu (1,oo)`

Explanation:

`ln` is continuous on its domain, so we need only make sure that `(x-1)/(x+2)` is in the domain of `ln`.

That is, we need `(x-1)/(x+2) > 0`

The quotient is positive for `x` in `(-oo,-2) uu (1,oo)`.