Answer
$f+g,f-g,fg$: all numbers greater than or equal to $0$; $\frac{f}{g}$: all numbers greater than or equal to $0$ except $4$
Work Step by Step
For all, the domain includes all numbers greater than or equal to $0$ since the number inside the square root must be positive. To find the second part of the domain of $\frac{f}{g}$, set the denominator equal to $0$.
$f+g=(\sqrt x)+(x-4)$
$f+g=\sqrt x+x-4$
$x\geq0$
$f-g=(\sqrt x)-(x-4)$
$f-g=\sqrt x-x+4$
$x\geq0$
$fg=(\sqrt x)(x-4)$
$fg=x\sqrt x-4$
$x\geq0$
$\frac{f}{g}=\frac{\sqrt x}{x-4}$
$x\geq0,x\ne4$
