Answer
$f(x)=|x+2|\sqrt[]{2}$
Work Step by Step
Using the properties of radicals, the given equation, $
f(x)=\sqrt[]{2x^2+8x+8}
,$ simplifies to
\begin{array}{l}\require{cancel}
f(x)=\sqrt[]{2(x^2+4x+4)}
\\\\
f(x)=\sqrt[]{2(x+2)^2}
\\\\
f(x)=\sqrt[]{(x+2)^2\cdot2}
\\\\
f(x)=|x+2|\sqrt[]{2}
\end{array}