The graph of a function $f$ is shown. $($The dashed lines indicate horizontal asymptotes.$)$

$$

$($i$)$

Find each of the following for the given function $g.($If an answer does not exist, enter DNE.$)$

$g(x)=\sqrt[\phantom{2}]{f(x)}$

$($a$)$ the domains of $g$ and $g^{\text{'}}($Enter your answer using interval notation.$)$

g

$g^{\text{'}}$

$($b$)$ the critical numbers of $g($Enter your answers as a comma$-$separated list.$)$

$x=$

$($c$)$ the approximate value of $g^{\text{'}}(6)($Round your answer to two decimal places.$)$

$g^{\text{'}}(6)=$