Please help. I think I'm close but I am just not getting the answer.

The problem reads:

Suppose the $\displaystyle f$ has an inverse and $\displaystyle f(2)=-4$, $\displaystyle f'(2)=\frac{3}{4}$. If $\displaystyle g=\frac{1}{f^-1}$, what is $\displaystyle g'(-4)$?

I have

$\displaystyle f^-1(-4)=2, f(2)=(-4)$

$\displaystyle g(-4)=\frac{1}{2}$

$\displaystyle g'(-4)=\frac{1}{f'(\frac{1}{2})}$

Thanks!