Question

How do you find the domain of `(x^2-x-12)^-4`?

Answer 1

`(x^2-x-12)^-4` can be written as `1/(x^2-x-12)^4`

This will be undefined if `(x^2-x-12) = 0`, but defined for all other values of `x` in `RR`.

`x^2-x-12 = (x-4)(x+3)` is zero when `x=4` or `x=-3`, so these are the only prohibited values of `x` and the domain of the function is:

`RR \\ {-3,4}`

that is `{x in RR: x != -3 ^^ x != 4}`