GATE 2024 MA – Question 28
For x,y>0, f(x,y)=(x²−y²,2xy). Let g be its local inverse near f(2,1). Find det Dg at f(2,1), to two decimals.
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Correct answer: 0.04 to 0.06
Explanation
$Df=\begin{pmatrix}2x&-2y\\2y&2x\end{pmatrix}$ has determinant 4(x²+y²)=20 at (2,1). The inverse Jacobian determinant is the reciprocal, giving **0.05**.