Definitions

1. The inverse function is the natural logarithm ln(x); because of this, some older sources refer to the exponential function as the anti-logarithm.
2. The inverse function is the function that "undoes" its original.
3. The inverse function, the angle subtended as a function of the arc length, is given by the elliptic functions. (Web site)
4. Its inverse function, the natural logarithm, ln(x), is defined for all positive x.
5. This inverse function is called the logarithmic function with base a. (Web site)

Natural Logarithm Function

1. The natural logarithm function is the inverse function of the exponential function. (Web site)

Algebraic Function

1. Writing x as a function of y gives the inverse function, also an algebraic function. (Web site)

Partial Inverse

1. It denotes the inverse function for sin(x) (actually a partial inverse; see below). (Web site)

Own Inverse Function

1. Also note that is its own inverse function, so to yield the natural logarithm of a certain number y, simply put in for x. (Web site)

Anti-Logarithm

1. In older sources it is often referred as an anti-logarithm which is the inverse function of a logarithm.

Tetration

1. The super- or hyper-4-logarithm is the inverse function of tetration.

Super-Logarithm

1. A super-logarithm or hyper-logarithm is the inverse function of the super-exponential function.
2. A super-logarithm or hyper-4-logarithm is the inverse function of tetration. (Web site)

Original Function

1. In other words, an inverse function undoes what the original function does.

Green

1. We plot the original function in Red, the Identity Function in Green, and the Inverse Function in Yellow. (Web site)

Proof

1. Idea of the proof: Redefine f to be the inverse function of g on the image of g to make it surjective. (Web site)

Mean

1. Thus f 3(x) may mean f(f(f(x))); in particular, f -1(x) usually denotes f 's inverse function.
2. In ring theory, the word involution is customarily taken to mean an antihomomorphism that is its own inverse function.

Output

1. An inverse function would output which child was born in a given year. (Web site)

Sense

1. The inverse function and the inverse image of a set coincide in the following sense. (Web site)

Graph

1. Graphic inverse, recognize the graph of an inverse function. (Web site)

Positive

1. Therefore its inverse function, the natural logarithm ln(x), is defined for all positive x.

Graphically

1. Graphically, this causes the inverse function to be a reflection of the original function across the line y=x (see figure 7 on p.205).

Derivative

1. The theorem also gives a formula for the derivative of the inverse function.

Key Pair

1. Second, each key in the key pair performs the inverse function of the other.

Reverse Order

1. The inverse function does the reverse of the original function in reverse order.

Analytic Function

1. The power series expansion of the inverse function of an analytic function can be determined using the Lagrange inversion theorem. (Web site)

Way

1. Viewed in this way, the base-b logarithm function is the inverse function of the exponential function b x. (Web site)
2. Viewed in this way, the base-b logarithm function is the inverse function of the exponential function bx. (Web site)
3. Implicit functions commonly arise as one way of describing the notion of an inverse function. (Web site)

Natural Logarithm

1. We can compute the derivative of the natural logarithm by using the general formula for the derivative of an inverse function.
2. The natural exponent is the inverse function of natural logarithm, so that.
3. The exponential function e x is the inverse function to the natural logarithm.

Certain Functions

1. For certain functions, we can write a symbolic representation of the inverse function. (Web site)

Exponential Function

1. This function is the inverse function of the exponential function, thus it holds e ln(x) = x for all positive x and ln(e x) = x for all real x.
2. Viewed in this way, the base- b logarithm function is the inverse function of the exponential function b x. (Web site)
3. See also density function; exponential function; hyperbolic function; inverse function; transcendental function.

Matrix Exponential

1. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. (Web site)

Definition

1. A compact way of rephrasing that definition is to say that the base- b logarithm function is the inverse function of the exponential function b x.
2. A compact way of rephrasing that definition is to say that the base-b logarithm function is the inverse function of the exponential function bx. (Web site)

Bijective Function

1. Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt.

Inverse Relation

1. Such functions do not have an inverse function, but they do have an inverse relation.
2. Stated otherwise, a function is invertible if and only if its inverse relation is a function, in which case the inverse relation is the inverse function. (Web site)
3. If an inverse function exists for a given function ƒ, it is unique: it must be the inverse relation. (Web site)

Inverse Function Theorem

1. Using the inverse function theorem, a derivative of a function's inverse indicates the derivative of the original function.
2. The inverse function theorem can be generalized to functions of several variables. (Web site)
3. Inverse function theorem, implicit function theorem and theorem on rank.

Differentiable

1. Moreover, the inverse function F − 1 is also continuously differentiable.
2. This is guaranteed to hold if φ is continuously differentiable by the inverse function theorem.

Jacobian

1. A necessary and sufficient condition for this inverse function to exist is that the determinant of the Jacobian should be different from zero. (Web site)

Injective

1. The trigonometric functions are periodic, and hence not injective, so strictly they do not have an inverse function.

One-To-One

1. A bi-Lipschitz function is a Lipschitz function T: U → R n which is one-to-one, and such that its inverse function T -1 T(U) → U is also Lipschitz.

Theorem

1. For a function between Euclidean spaces, the inverse function theorem gives a sufficient condition for the function to have a locally defined inverse.
2. Hello, I am stuck right at the beginning of a proof of the inverse function theorem.
3. This is a generalization of the inverse function theorem to maps between manifolds. (Web site)

Implicit

1. For example, there are versions of the implicit and inverse function theorems for such functions.
2. For example, there are versions of the implicit and inverse function theorem s for such functions. (Web site)

Lambert

1. The Lambert W function is the inverse function of ƒ(w) = we w. (Web site)

Bijective

1. Therefore to define an inverse function we must restrict their domains so that the trigonometric function is bijective. (Web site)

Bijection

1. If a function is a bijection, then it has an inverse function. (Web site)
2. If the homomorphism is a bijection whose inverse function is also a graph homomorphism, then f is a graph isomorphism. (Web site)

Exponential

1. Like most functions you are likely to come across, the exponential has an inverse function, which is log e x, often written ln x (pronounced "log x").

Logarithm

1. A double logarithm, or iterated logarithm, ln(ln(x)), is the inverse function of the double exponential function.
2. For p -adic numbers, the logarithm can also be defined as the inverse function of the exponential. (Web site)
3. The inverse function to exponentiation with base b (when it is well-defined) is called the logarithm with base b, denoted log b.

Function

1. A function may also be described through its relationship to other functions, for example, as the inverse function or a solution of a differential equation. (Web site)
2. Sometimes, a function is described through its relationship to other functions (see, for example, inverse function).
3. In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.

Inverse

1. Inverse of a function: some functions have an inverse function. (Web site)
2. Another approach is to define tetration over real heights as the inverse of the super-logarithm, which is its inverse function with respect to the height.
3. In the same way as for the image, some authors use square brackets to avoid confusion between the inverse image and the inverse function. (Web site)

Inverse Function

1. Every bijection has an inverse function that undoes its action, and thus each element of a symmetric group does have an inverse.
2. Inverse function If a function f: X → Y is bijective then preimages of any element y in the codomain Y is a singleton.
3. According to the inverse function theorem, the matrix inverse of the Jacobian matrix of a function is the Jacobian matrix of the inverse function.

Categories

1. Information > Science > Mathematics > Exponential Function
2. Function > Logarithm > Logarithms > Natural Logarithm
3. Inverse
4. Trigonometric Functions
5. Bijection
6. Books about "Inverse Function" in Amazon.com
   

Continue: More Keywords - - - - - - - - - -