Answer
$-\pi^{2}+4\pi+1$
Work Step by Step
We are given that $g(x)=-x^{2}+4x+1$. In order to evaluate the function at $x=\pi$, we can plug in $\pi$ to the function and evaluate directly.
$g(\pi)=-x^{2}+4x+1=-(\pi)^{2}+4(\pi)+1=-\pi^{2}+4\pi+1$