What does it mean when $f(x_1, x_2) = x_1 + x_2$ on $\Bbb R \times \Bbb R_{++}$

Question

Does that mean that $x_1$ is all real numbers and $x_2$ is restricted to only positive numbers?

Answer 1

Normally, $\mathbb{R}_+$ and $\mathbb{R}^+$ denote the set of positive reals. so you are correct, $f$ on $\mathbb{R} \times \mathbb{R}^+$ means the first variable is a real number and the second -- a positive real number.