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 <span><span>f<span>(w)</span></span>=3<span>w9</span></span>. You need to find out the values of w for which <span><span>f<span>(w)</span></span>=0</span>. You have
<span><span>f<span>(w)</span></span>=0⇔3<span>w9</span>=0⇔<span>w9</span>=0⇔w<span>=9</span><span>√0</span>=0</span>
So, your only problem is <span>w=0</span>, and all other numbers are fine.
Your domain is thus given by the set <span>{x∈R∣x≠0}</span>
The domain can also be written as <span><span>(−∞,0)</span>∪<span>(0,+∞)</span></span>.
