#### Answer

$-\frac{1}{x^{2}}+\frac{4}{x}+1$

#### Work Step by Step

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