To define the domain formed by combining the three given sets, we need to identify all the unique elements present in any of the sets. The domain is essentially the union of the three sets, meaning it includes every distinct element from all sets combined.
Let's examine the sets given:
1. [tex]\(\{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8\}\)[/tex]
2. [tex]\(\{-3, -1, 1, 3, 6\}\)[/tex]
3. [tex]\(\{3, -1, 2, 0, -2\}\)[/tex]
We will list all unique elements from these sets:
- The first set [tex]\(\{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8\}\)[/tex] contains:
[tex]\(-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8\)[/tex].
- The second set [tex]\(\{-3, -1, 1, 3, 6\}\)[/tex] contains:
[tex]\(-3, -1, 1, 3, 6\)[/tex]. These elements are [tex]\(-3, -1, 1, 3, 6\)[/tex] which are already present in the first set.
- The third set [tex]\(\{3, -1, 2, 0, -2\}\)[/tex] contains:
[tex]\(3, -1, 2, 0, -2\)[/tex]. These elements are all present in the first set too.
By combining all these unique elements, we can write the domain:
[tex]\[\{0, 1, 2, 3, 4, 5, 6, 7, 8, -2, -3, -1\}\][/tex]
Thus, the domain of the union of the three sets is:
[tex]\[\boxed{\{0, 1, 2, 3, 4, 5, 6, 7, 8, -2, -3, -1\}}\][/tex]
