Find the Domain of \( fg \)
Question:
Let \(f\) and \(g\) be two real functions given by
\[ f=\{(0,1),(2,0),(3,-4),(4,2),(5,1)\} \]
and
\[ g=\{(1,0),(2,2),(3,-1),(4,4),(5,3)\} \]
Find the domain of
\[ fg \]
Solution:
Domain of \(f\):
\[ \{0,2,3,4,5\} \]
Domain of \(g\):
\[ \{1,2,3,4,5\} \]
Domain of \(fg\) is the common domain of \(f\) and \(g\).
Therefore,
\[ \{0,2,3,4,5\}\cap\{1,2,3,4,5\} \]
\[ =\{2,3,4,5\} \]
Hence,
\[ \boxed{\{2,3,4,5\}} \]