Answer
$g\left( -x \right)=-x^2-4x+1$
Work Step by Step
Substituting $x$ with $
-x
$ in the given function, $
g(x)=-x^2+4x+1
,$ then,
\begin{array}{l}\require{cancel}
g\left( -x \right)=-\left( -x \right)^2+4\left( -x \right)+1
\\\\
g\left( -x \right)=-x^2-4x+1
.\end{array}