Find the Domain of \(f+g\)
Question
Let \(f\) and \(g\) be two functions given by
\[ f=\{(2,4),(5,6),(8,-1),(10,-3)\} \]and
\[ g=\{(2,5),(7,1),(8,4),(10,13),(11,-5)\} \]Then, the domain of \(f+g\) is __________.
Solution
The domain of \(f+g\) consists of all elements that belong to both domains of \(f\) and \(g\).
Domain of \(f\)
The first elements of ordered pairs in \(f\) are:
\[ \{2,5,8,10\} \]Domain of \(g\)
The first elements of ordered pairs in \(g\) are:
\[ \{2,7,8,10,11\} \]Domain of \(f+g\)
The domain of \(f+g\) is the intersection of the domains of \(f\) and \(g\).
\[ \{2,5,8,10\}\cap\{2,7,8,10,11\} \] \[ =\{2,8,10\} \]