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

1 Answer
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(w)=3w^9#. You need to find out the values of #w# for which #f(w)=0#. You have
#f(w)=0 \iff 3w^9=0 \iff w^9=0 \iff w=^9\sqrt0=0#

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

Your domain is thus given by the set #{x \in \mathbb{R} | x \ne 0}#

The domain can also be written as #(-oo,0)uu(0,+oo)#.