(3) If the function $f(x)=a+\frac{3}{x-b}$ is the inverse of the function $g(x)=1+\frac{c}{2 x+1}$, find the values of $a$, $b$, and $c$.
\begin{array}{l}\text { (3) } a=-\frac{1}{2}, b=1, \\ c=6\end{array}