#### Answer

$g(\frac{1}{2})=\frac{11}{4}=2.75$

#### Work Step by Step

To find the value of $g(\frac{1}{2})$, substitute $\frac{1}{2}$ to $x$ in $g(x)$ to obtain:
$g(x)=-x^2+4x+1
\\g(\frac{1}{2})=-(\frac{1}{2})^2+4(\frac{1}{2})+1
\\g(\frac{1}{2})=-\frac{1}{4}+2+1
\\g(\frac{1}{2})=-\frac{1}{4}+3
\\g(\frac{1}{2})=-\frac{1}{4}+\frac{12}{4}
\\g(\frac{1}{2})=\frac{11}{4}=2.75$