Question

How do you find the domain of `ln(x^2-4)`?

Answer 1

The domain of `f(x)` is `(-oo,-2) uu (+2,+oo)`

Explanation:

`f(x)= ln(x^2-4)`

Since `lnx` is defined for `x>0`
`f(x)` is defined for `x^2-4 >0`

Hence: `f(x)` is defined for `absx> 2`

The domain of a function is the set of input values `(x)` for which the function `f(x)` is defined.

Therefore the domain of `f(x)` in this example is: `(-oo,-2) uu (+2,+oo)`

This can be seen by the graph of `f(x)` below.
graph{ln(x^2-4) [-10, 10, -5, 5]}