Answer
$$\color{blue}{\bf{ (-\infty, \infty) }}$$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = x + 1}$ and $\bf{g(x) = x^2}$
and asked to find the $\bf{domain}$ of $f+g$
$f(x) +g(x) = x + 1 + x^2$
$x + 1 + x^2$
$x$ can be any real number so the domain of $f+g$ is:
$$\color{blue}{\bf{ (-\infty, \infty) }}$$
