Answer
$\frac{11}{4}$
Work Step by Step
We are given that $g(x)=-x^{2}+4x+1$. We can plug the given value into the equation and evaluate.
$g(\frac{1}{2})=-(\frac{1}{2})^{2}+4(\frac{1}{2})+1=-(\frac{1}{4})+2+1=-\frac{1}{4}+2+1=-\frac{1}{4}+\frac{8}{4}+\frac{4}{4}=\frac{-1+8+4}{4}=\frac{11}{4}$
