Question

What is the domain and range of `ln(1-x^2)`?

Answer 1

Domain: `{x|-1< x <1}` or in interval notation `(-1,1)`

Range: `{y|y<=0}` or in interval notation `(-oo, 0]`

Explanation:

`ln(1-x^2)`

The input to the natural log function must be greater than zero:

`1-x^2>0`

`(x-1)(x+1)>0`

`-1< x <1`

Therefore Domain is:

`{x|-1< x <1}` or in interval notation `(-1,1)`

At zero the value of this function is `ln(1) = 0` and as `x->1` or as `x-> -1` the function `f(x) -> -oo` is the range is:

`{y|y<=0}` or in interval notation `(-oo, 0]`

graph{ln(1-x^2) [-9.67, 10.33, -8.2, 1.8]}