Find the Domain of \(fg\)
Question
Let \(f\) and \(g\) be two real functions given by
\[ f=\{(10,1),(2,0),(3,-4),(4,2),(5,1)\} \]and
\[ g=\{(1,0),(2,3),(3,-1),(4,4),(5,3)\} \]Then the domain of \(fg\) is given by __________.
Solution
The domain of the product \(fg\) consists of all elements which belong to both domains of \(f\) and \(g\).
Domain of \(f\)
The first elements of ordered pairs in \(f\) are:
\[ \{10,2,3,4,5\} \]Domain of \(g\)
The first elements of ordered pairs in \(g\) are:
\[ \{1,2,3,4,5\} \]Domain of \(fg\)
The domain of \(fg\) is the intersection of the domains of \(f\) and \(g\).
\[ \{10,2,3,4,5\}\cap\{1,2,3,4,5\} \] \[ =\{2,3,4,5\} \]