Given, $f :\mathrm{R^2} \to\mathrm{R^2}$ , $f(x,y)= (e^x(y^2- 4x+ 9), x \log (y^2 +9) +y).$ Find $f^{-1}(x,y)$ and $Df^{-1}(x,y)$ at point $(2,0).$
Here, I'm unable to just substitute $u$ and $v$ in place of coordinates for $f(x,y)$,
also in terms of basis for $\mathrm{R^2}$, finding $f(1,0)$ and $f(0,1)$ and then obtaining matrix for $f$ and $f^{-1}$. Is that a valid process?