# Question about proof of the inverse function theorem

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!

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