#### Answer

$g+h$ and $g\cdot h$ both have $\mathbb{R}$ as their domain.

#### Work Step by Step

The domain of $g+h$ is the intersection of domains of g and of h.
The domain of $g\cdot h$ is the intersection of domains of g and of h.
Both g and h are defined on $\mathbb{R}$ so,
$g+h$ and $g\cdot h$ both have $\mathbb{R}$ as their domain.