  We apply the density of states approach to the Z(3) spin model with a
chemical potential mu. For determining the density of states we use restricted
Monte Carlo simulations on small intervals of the variable for the density. In
each interval we probe the response of the system to the variation of a free
parameter in the Boltzmann factor. This response is a known function which we
fit to the Monte Carlo data and the parameters of the density are obtained from
that fit (functional fit approch; FFA). We evaluate observables related to the
particle number and the particle number susceptibility, as well as the free
energy. We find that for a surprisingly large range of mu the results from the
FFA agree very well with the results from a reference simulation in the dual
formulation of the Z(3) spin model which is free of the complex action problem.
