Answer
(a) The domain is $A\cap B$.
(b) The domain is $A\cap B$.
(c) The domain is $A\cap B\setminus\{x_0|g(x_0)=0\}$.
Work Step by Step
(a) We can sum only where both $f$ and $g$ are defined so the domain of $f+g$ is $A\cap B$.
(b) We can multiply only where both $f$ and $g$ exist so the domain of $fg$ is $A\cap B$.
(c) We can divide only where both $f$ and $g$ are defined BUT since we cannot divide by zero we have to exclude all points $x_0$ such that $g(x_0)=0$ which can be written as $A\cap B\setminus\{x_0|g(x_0)=0\}$.
