inverse

(noun)

a function that undoes another function

Related Terms

Examples of inverse in the following topics:

  • Inverse Functions

    • An inverse function is a function that undoes another function.
    • Stated otherwise, a function is invertible if and only if its inverse relation is a function on the range $Y$, in which case the inverse relation is the inverse function.
    • Not all functions have an inverse.
    • Thus, the inverse of $x^2+2$ is $\sqrt{x-2}$.
    • A function $f$ and its inverse, $f^{-1}$.

  • Inverse Functions

    • An inverse function is a function that undoes another function: For a function $f(x)=y$ the inverse function, if it exists, is given as $g(y)= x$.
    • A function $f$ that has an inverse is called invertible; the inverse function is then uniquely determined by $f$ and is denoted by $f^{-1}$ (read f inverse, not to be confused with exponentiation).
    • Not all functions have an inverse.
    • Inverse operations are the opposite of direct variation functions.
    • A function $f$ and its inverse $f^{-1}$.

  • Inverse Trigonometric Functions: Differentiation and Integration

    • It is useful to know the derivatives and antiderivatives of the inverse trigonometric functions.
    • The inverse trigonometric functions are also known as the "arc functions".
    • There are three common notations for inverse trigonometric functions.
    • They can be thought of as the inverses of the corresponding trigonometric functions.
    • The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.

  • Continuity

    • A continuous function with a continuous inverse function is called "bicontinuous."

  • Hyperbolic Functions

    • The inverse hyperbolic functions are the area hyperbolic sine "arsinh" (also called "asinh" or sometimes "arcsinh") and so on.

  • Models Using Differential Equations

    • The decay constant, $\lambda$ ("lambda"), is the inverse of the mean lifetime.

  • The Natural Exponential Function: Differentiation and Integration

    • Note that the exponential function $y = e^{x}$ is defined as the inverse of $\ln(x)$.

  • Planetary Motion According to Kepler and Newton

    • In addition, the magnitude of the acceleration is inversely proportional to the square of its distance from the Sun.
    • Therefore, by Newton's law, every planet is attracted to the Sun, and the force acting on a planet is directly proportional to the mass and inversely proportional to the square of its distance from the Sun.

  • Bases Other than e and their Applications

    • It is the inverse function of $n \Rightarrow 2^n$.

  • Basic Integration Principles

    • Integration is an important concept in mathematics and—together with its inverse, differentiation—is one of the two main operations in calculus.