Find the domain of the function $f+g$, where $f(x)=\sqrt{4-x}$ and $g(x)=x^2$ for $x\in\mathbb{R}$?

Question

I know that Dom$ (f) = (-\infty,4]$ Dom $(g) = \mathbb{R}$, but the problem is Dom$(f+g)$.

Please also tell Dom$(f-g)$

Answer 1

Since $g(x)=x^2$ does exists for every $x in \mathbb R$ and since $\sqrt{4-x}$ require that $4-x \geq 0$, the Domain of $f+g$ is simply

$$ D = \left\{ {x \in \mathbb{R}:x \geqslant 4} \right\} $$