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**1. Homework Statement**

Could you please help me with this problem?

Let f(x) = (f_1(x), f_2(x)) map R[tex]^{2}[/tex] into itself where f_1, f_2 have continuous 1st/ 2nd partial derivatives in each variable. Assume that f maps origin to itself and that J_f(x)(Jacobian matrix) is an invertible 2x2 matrix for all x. Put g(x) = x - f'(x)[tex]^{-1}[/tex].f(x)

(i) Explicitly compute J_g(x) using relation J_f[tex]^{-1}[/tex]. J_f = Identity matrix I[tex]_{2}[/tex]

Thanks in advance!!!

**2. Homework Equations**

**3. The Attempt at a Solution**

What are f'(x)[tex]^{-1}[/tex] and f'(x)[tex]^{-1}[/tex].f(x)

? I am just having trouble with the notations.

Can you give me hints?

( For some reason, I can't you tex right???)[tex]^{}[/tex]

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