Question

When is d ⊂ rn → rn f : called locally invertible? Is the function f given by f( )( ) x, y,z = x + y + z, x − 2y + 3z, x + y −1 locally invertible at (0,1,2)? Justify your answer?

Answer 1

Answer:

The 'f' is locally invertible for the function so that

The Local invertible refers with an affine approximation for the point of invertible to there closest affine. So at the end of given function, it will get derivative through plus.

Otherwise, we can solve through the Jacobian process. So the differential  will be denoted by ∇ f(x), for various subdifferentials as well.