Answer
$g\left( -\dfrac{1}{4} \right)=-\dfrac{1}{16}$
Work Step by Step
Substituting $x$ with $
-\dfrac{1}{4}
$ in the given function, $
g(x)=-x^2+4x+1
,$ then,
\begin{array}{l}\require{cancel}
g\left( -\dfrac{1}{4} \right)=-\left( -\dfrac{1}{4} \right)^2+4\left( -\dfrac{1}{4} \right)+1
\\\\
g\left( -\dfrac{1}{4} \right)=-\dfrac{1}{16}-1+1
\\\\
g\left( -\dfrac{1}{4} \right)=-\dfrac{1}{16}
.\end{array}