operations on real functions

If $f$ and $g$ are two real functions such that domain of $f$ is $D_1$ and domain of $g$ is $D_2$ both being subsets of $\mathbb R$ . My book says that the function $f+g$ will have the domain ($D_1 \cap D_2$). Why is this? And if $f$ and $g$ have co-domain $C_1$ and $C_2$ respectively such that $C_1$ and $C_2$ are subsets of set of real numbers then what will be the co-domain of $f+g$?