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I am studying this proof (see picture) of the implicit function theorem in multivariable analysis. I understand the proof, but I do not understand why we can assume without loss of generality that $x_0=y_0=0$and f'(0)=Id. I saw in another topic that they gave the hint $F(x)=f'(x_0)^{-1}(f(x+x_0)-y_0)$, but I don't know how to use this. Could somebody please help me? Thank you! enter image description here

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  • $\begingroup$ Then $F(0)=0$ and $F'(0)=\text{Id}$. $\endgroup$ – Angina Seng Dec 2 '19 at 7:59
  • $\begingroup$ @LordSharktheUnknown What does that imply? $\endgroup$ – Rien Dec 2 '19 at 8:01

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