(Solved): please solve this  The graph of a function \( f \) is shown. (The dashed lines indicate horizon ...

The graph of a function \( f \) is shown. (The dashed lines indicate horizontal asymptotes.) Find each of the following for the given function \( g \). (If an answer does not exist, enter DNE.) \[ g(x)=\sqrt{f(x)} \] (a) the domains of \( g \) and \( g^{\prime} \) (Enter your answer using interval notation.) (b) the critical numbers of \( g \) (Enter your answers as a comma-separated list.) \[ x= \] (c) the approximate value of \( g^{\prime}(6) \) (Round your answer to two decimal places.) \[ g^{\prime}(6)= \] (d) all vertical and horizontal asymptote(5) of \( g \) (Enter your answers as a comma-separated list.) vertical asymptote(s) \( x= \) horizontal asymptote(s) \( \quad y= \)