Let $F(x)=\frac{x2}{\sqrt[\phantom{2}]{x2}}.$ Make sure to show complete and correct work to carn full credit.

$($a$)$ Determine the domain of $F(x).$

$($b$)$ Evaluate $F(4)$

$($c$)$ Find a number $b$ such that $F(b)=3.$

$($d$)$ Determine the average rate of change of $F(x)$ from $x_1=2$ to $x_2=7.$