Solving SDE with Let f(x) and Showing (f^{-1})',(f^{-1})

[secuK]

SDE
$d_t=\frac{1}{2}\sigma(X_t)\sigma'(X_t)d_t+\sigma(X_t)dW_t$
$X_0=x_0$
i) Let $f(x)=\int^x_{x_0}\frac{dy}{\sigma(y)}$
and show $(f^{-1})',(f^{-1})''$.
ii) Use i) and solve SDE.

 

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