Let \(N_1\) denote the class of Nevanlinna analytic functions \[ w=f(z)= \int^1_{-1} {d\mu(t)\over z-t}= \sum^\infty_{n=1} {a_n\over z^n}, \quad z\notin [-1,1], \] where \(\mu(t)\) is a probability measure on \([-1,1]\). Also let \(N_2\) denote the class of associated analytic functions \[ w=\varphi (z)=f \left({1\over z}\right) =\int^1_{-1} {zd\mu(t) \over 1-tz}= \sum^\infty_{n =1} a_nz^n, \quad z\notin\mathbb{R} \setminus(-1,1). \] In this paper the author obtains the extremum of a typical functional in the class \(N_2\) and it is proved its application for the determination of the extremum of coefficients of the inverse functions of the Nevanlinna univalent functions of the class \(N_2\). Finally the work concludes with a conjecture related to these coefficients.