Question

How do you find the domain of `f(x)=(-3x^2)/(x^2+4x-45)`?

Answer 1

Domain: all Real values except `(-9)` and `(+5)`

Explanation:

`f(x)=(-3x^2)/(x^2+4x-45)`
`color(white)("XXX")`will be defined for all Real values of `x`
`color(white)("XXX")`except those values which cause the denominator to be equal to zero.

That is the Domain will be all `RR`
except when
`color(white)("XXX")x^2+4x-45=0`

Factoring:
`color(white)("XXX")(x+9)(x-5)=0`

So the Domain of `f(x)` is
`color(white)("XXX")RR-{-9,+5}`