Answer
$\displaystyle \frac{1}{2}$
Work Step by Step
Apply Th.1: the derivative rule for inverses.
If $f(b)=a$, then
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=a}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=b}}$
We are given $f(0)=0,$ (graph passes through (0,0))
$\Rightarrow\qquad a=0, \qquad b=0$
and the slope at the point ($0,0$) ... (at $x=0$) is
$\left.\frac{df}{dx}\right|_{x=0}=2$
$\displaystyle \left.\frac{df^{-1}}{dx}\right|_{x=0}\ \ =\ \ \frac{1}{\left.\frac{df}{dx}\right|_{x=0}}=\frac{1}{2}$
