#### Answer

$ g(x(w)) =4\sqrt{7} e^{w}$ and $g(x(w)) =4\sqrt{7} e^{2}$

#### Work Step by Step

Given $$
g(x)=\sqrt{7 x^{2}} ; x(w)=4 e^{w}
$$
Since $g(x(w))$ given by
\begin{align*}
g(x(w))&=\sqrt{7 (x(w))^{2}} \\
&=\sqrt{7 (4 e^{w})^{2}} \\
&=4\sqrt{7} e^{w}
\end{align*}
and $g(x(w)) =4\sqrt{7} e^{2}$