Question

Find the domain of the rational function:
g(x)=x/x^2-9

Answer 1

\[g(x)=\frac{x}{x^2-9}\]

Answer 2

the domain is the x-values, so you look at when x does not exist. You cannot divide by zero, so \[x^2-9\neq0\].
you can factor this:\[(x+3)(x-3)\neq0\]
so, \[x \neq3\] and \[x \neq-3\]
Thus the domain is all the x-values except \[x=3\] and \[x=-3\]
In interval notation, that is \[(-\infty,-3)U(-3,3)U(3,\infty)\]

Answer 3

I would have also accepted
\[{x|x \neq -3, x \neq 3}\]
but thank you.