Re: Help inverse function theorem
- From: "Carl R." <solrac140@xxxxxxxxxxx>
- Date: Mon, 15 Dec 2008 13:56:21 -0800 (PST)
On 15 dic, 14:13, "Carl R." <solrac...@xxxxxxxxxxx> wrote:
Let f= (f_1, f_2, f_3) be a vector valued function defined (for every
point (x_1,x_2,x_3) in R^3 for which
x_1 + x_2 + x_3 is not equal to -1) as follows:
f_k (x_1,x_2,x_3) = x_k /( 1+x_1+x_2+x_3) where k =1,2,3.
After some computations I found that the determinant of the Jacobian
matrix is (1+x_1+x_2+x_3)^(-4) (which
coincides with the answer of the book).
Then, by the inverse function theorem, it follows that f is one to one
since the determinant is nonzero.
The problem is the following:
Compute f^(-1) explicitly.
How can I do this????
http://en.wikipedia.org/wiki/Inverse_function_theorem
gives a formula to find the inverse of the jacobian matrix, but I'm
trying to find the inverse of the function.
How to do this?
Nevermind , I figured this out. Its just a system of equations :)
.
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- From: Carl R.
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