$\underset{x\to 3}{\mathop{\lim }}\,\frac{f(x)-4}{x-3}\times \underset{x\to 3}{\mathop{\lim }}\,\frac{1}{x+3}=2\Rightarrow \underset{x\to 3}{\mathop{\lim }}\,\frac{f(x)-4}{x-3}=12\Rightarrow \left\{ \begin{matrix}    f(3)=4  \\    {f}'(3)=12  \\ \end{matrix} \right.$  ${g}'(x)=\frac{3{f}'(3x)\sqrt{x}-\frac{1}{2\sqrt{x}}f(3x)}{x}$  ${g}'(1)=3{f}'(3)-\frac{f(3)}{2}=3\times 12-2=34$