2021 AMC 12B Problem 16

Let g(x) be a polynomial with leading coefficient 1, whose three roots are the reciprocals of the three roots of f(x)=x^3+ax^2+bx+c, where 1<a<b<c. What is g(1) in terms of a,b, and c?

\textbf{(A) }\frac{1+a+b+c}c \qquad \textbf{(B) }1+a+b+c \qquad \textbf{(C) }\frac{1+a+b+c}{c^2}\qquad \textbf{(D) }\frac{a+b+c}{c^2} \qquad \textbf{(E) }\frac{1+a+b+c}{a+b+c}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.