Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you find the domain of $f (x) = \frac{- 3 x^{2}}{x^{2} + 4 x - 45}$ $f(x)=(-3x^2)/(x^2+4x-45)$ ?

1 Answer

Aug 5, 2016

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

Explanation:

$f (x) = \frac{- 3 x^{2}}{x^{2} + 4 x - 45}$ $f(x)=(-3x^2)/(x^2+4x-45)$
$XXX$ $color(white)("XXX")$ will be defined for all Real values of $x$ $x$
$XXX$ $color(white)("XXX")$ 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
$color(white)("XXX")RR-{-9,+5}$

Related questions

See all questions in Domain and Range of a Function

Impact of this question

1613 views around the world

You can reuse this answer
Creative Commons License