Question

How do you find the domain for `f(x) = (4x^2 - 9)/(x^2 + 5x + 6)`?

Answer 1

To find the domain, we only need to factor the denominator to find its zeros. Other than the denominator being zero, `f(x)` is well defined for all `x in RR`.

`x^2+5x+6 = (x+3)(x+2)`

which is zero when `x = -3` or `x=-2`

So the domain of `f(x)` is:

`(-oo, -3) uu (-3, -2) uu (-2, oo)`

That is `{x in RR : x != -3 and x != -2}`