Question

What is the domain of `f(x) = (x^2 - x - 6) /( x^2 + x - 12)`?

Answer 1

Domain: `RR-{-4,+3}`

Explanation:

`f(x)=(x^2-x-6)/(x^2+x-12)`
is defined for all Real values of `x` except those that cause `x^2+x-12 = 0`

Since `(x^2+x-1) = (x+4)(x-3)`

`color(white)("XXX")x=-4` and `x=3`
cause `x^2+x-12=0`
and are therefore forbidden from the Domain of `f(x)`