Question

How do you find the domain of `f(x)=(x-2)/(x+4)`?

Answer 1

The only restriction on the domain comes from the `(x+4)` denominator, which cannot be zero.

So the domain is `RR` \ `{-4}`.

In interval notation: `(-oo, -4) uu (-4, oo)`

Explanation:

`(x - 2)` is well defined for all `x in RR`

`(x + 4)` is well defined for all `x in RR`

So `f(x) = (x-2)/(x+4)` is well defined,

except when the denominator `(x+4) = 0`,
which happens when `x = -4`.