F represents the holomorphic polynomial z³−3z. Its real Jacobian determinant is $|3z^2-3|^2$, zero exactly at z=1 and z=−1. Everywhere else F is locally invertible. **C**.
More Multivariable Analysis questions
GATE 2024 MA Q28– For x,y>0, f(x,y)=(x²−y²,2xy). Let g be its local inverse near f(2,1). Find det Dg at…
GATE 2021 MA Q50– The equation xy−z log y+e(xz)=1 defines y=f(x,z) near (x,y,z)=(0,1,1). Find ∇f(0,1).
GATE 2026 MA Q16– f: R2 R2 is f(x,y)=(ex y,ex y). Which statement is true?