Question

How can we check local invertible function of two variable?

Answer 1

Answer:

In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. The theorem also gives a formula for the derivative of the inverse function. In multivariable calculus, this theorem can be generalized to any continuously differentiable, vector-valued function whose Jacobian determinant is nonzero at a point in its domain, giving a formula for the Jacobian matrix of the inverse. There are also versions of the inverse function theorem for complex holomorphic functions, for differentiable maps between manifolds, for differentiable functions between Banach spaces, and so forth

Step-by-step explanation:

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Answer 2

Answer:

You can check to see whether a function is invertible by using the horizontal line test on its graph. If there does not exist a horizontal line on the plane that travels through more than one point on the graph, then the function of that graph is invertible (because each value is mapped to a single value).

.......... . function........

STEP 1: Stick a "y" in for the "f(x)" guy:

STEP 2: Switch the x and y. ( because every (x, y) has a (y, x) partner! ):

STEP 3: Solve for y:

STEP 4: Stick in the inverse notation, continue. 123.