Univalency of certain transform of univalent functions

We consider univalency problem in the unit disc $\mathbb{D}$ of the function $$g(z)=\frac{(z\mathrm{/}f(z))-1}{-a_2},$$ where $f$ belongs to some classes of univalent functions in $\mathbb{D}$ and $a_2=\frac{f^{\mathrm{\prime }\mathrm{\prime }}(0)}{2}\mathrm{\ne }0$.