  Ma-Minda class (of starlike functions) consists of all normalized analytic
functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is
contained in the some starlike region in the right-half plane. We obtain the
best possible bounds on the second and third coefficient for the inverse
functions of functions in the Ma-Minda class. The bounds on the Fekete-Szeg\"o
functional and the second Hankel determinant of the inverse functions of the
functions belonging to the Ma-Minda class are also determined. Further, the
bounds on the first five coefficients of the inverse functions are investigated
for two particular subclasses of the Ma-Minda class. In addition, some radius
estimates associated with the two subclasses are also computed.
