# What is the domain of the function p(w)=2/(3w^9)?

Jan 23, 2015

You have a fractions, so the only thing you must be sure of is that the denominator is not zero.

In your case, the denominator is given by the function $f \left(w\right) = 3 {w}^{9}$. You need to find out the values of $w$ for which $f \left(w\right) = 0$. You have
$f \left(w\right) = 0 \setminus \iff 3 {w}^{9} = 0 \setminus \iff {w}^{9} = 0 \setminus \iff w {=}^{9} \setminus \sqrt{0} = 0$

So, your only problem is $w = 0$, and all other numbers are fine.

Your domain is thus given by the set $\left\{x \setminus \in \setminus m a t h \boldsymbol{R} | x \setminus \ne 0\right\}$

The domain can also be written as $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$.