I have a function

$\displaystyle f(x) = 4x^2 - x^3$

If the domain of this function is restricted to 0 < x < 8/3 then f-1(x) can be defined - ie inverse function.

I am told to find the gradient of $\displaystyle f^-1(x)$ at the point ($\displaystyle \frac{7}{8}, \frac{1}{2}$)

My first thought was to work out the inverse function. But this looks hard? Is this what I should do? Or is there another way? I know that an inverse function is a reflection of function on y=x - can I somehow use this to calculate? If so how?

Angus