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
\[ g=\{(2,5),(7,1),(8,4),(10,13),(11,-5)\} \]
Find the domain of
\[ f+g \]
Solution:
Domain of \(f\):
\[ \{2,5,8,10\} \]
Domain of \(g\):
\[ \{2,7,8,10,11\} \]
Domain of \(f+g\) is the common domain of \(f\) and \(g\).
Therefore,
\[ \{2,5,8,10\}\cap\{2,7,8,10,11\} \]
\[ =\{2,8,10\} \]
Hence,
\[ \boxed{\{2,8,10\}} \]