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  2. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}

  3. Inverse function theorem - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_theorem

    For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point ; then is injective (or bijective onto the image) in a neighborhood of , the inverse is continuously differentiable near = (), and the derivative of the inverse function at is the reciprocal of the derivative of at : ′ = ′ = ′ (()).

  4. Invertible matrix - Wikipedia

    en.wikipedia.org/wiki/Invertible_matrix

    The linear transformation mapping x to Ax is invertible, i.e., has an inverse under function composition. (Here, again, "invertible" can equivalently be replaced with either "left-invertible" or "right-invertible") The transpose A T is an invertible matrix. A is row-equivalent to the n-by-n identity matrix I n.

  5. Bijection - Wikipedia

    en.wikipedia.org/wiki/Bijection

    A function is bijective if and only if it is invertible; that is, a function : is bijective if and only if there is a function :, the inverse of f, such that each of the two ways for composing the two functions produces an identity function: (()) = for each in and (()) = for each in .

  6. Inverse element - Wikipedia

    en.wikipedia.org/wiki/Inverse_element

    An homomorphism of algebraic structures is an isomorphism if and only if it is a bijection. The inverse of a bijection is called an inverse function. In the other cases, one talks of inverse isomorphisms. A function has a left inverse or a right inverse if and only it is injective or surjective, respectively. An homomorphism of algebraic ...

  7. The best under-$50 clothing items to buy at Amazon right now

    www.aol.com/the-best-under-50-clothing-items-to...

    Style meets function with a hidden key pocket, two smartphone pockets, and interlock seams that minimize chafing and rubbing. "These are the most comfortable pants I have ever worn," raved one ...

  8. Aaron Rodgers Is ‘a Very Difficult Person to Understand ...

    www.aol.com/aaron-rodgers-very-difficult-person...

    Chopra says Rodgers was immediately “really trusting” with him and Hughes, adding that throughout their year working together on the documentary, Rodgers “was very open and vulnerable.”

  9. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...