Inverse Function

In mathematics, an inverse function is a function that undoes another function: If an input x into the function ƒ produces an output y, then putting y into the inverse function g produces the output x, and vice versa. i.e., ƒ(x)=y, and g(y)=x. More directly, g(ƒ(x))=x, meaning g(x) composed with ƒ(x) leaves x unchanged.

A function ƒ that has an inverse is called invertible; the inverse function is then uniquely determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with exponentiation).

Other articles related to "inverse function, function, inverse, inverse functions, functions":

Inverse Functions - Inverses in Calculus - Formula For The Inverse
... For example, if ƒ is the function then we must solve the equation y = (2x + 8)3 for x Thus the inverse function ƒ−1 is given by the formula Sometimes the ... For example, if ƒ is the function then ƒ is one-to-one, and therefore possesses an inverse function ƒ−1 ... The formula for this inverse has an infinite number of terms ...
Logrithm - Analytic Properties - Inverse Function
... Therefore, the logarithm to base b is the inverse function of f(x) = bx ... Inverse functions are closely related to the original functions ... In that case, logb(x) is an increasing function ...
Logrithm - Generalizations - Inverses of Other Exponential Functions
... Exponentiation occurs in many areas of mathematics and its inverse function is often referred to as the logarithm ... For example, the logarithm of a matrix is the (multi-valued) inverse function of the matrix exponential ... Another example is the p-adic logarithm, the inverse function of the p-adic exponential ...
Inverse Function - Generalizations - Preimages
... If ƒ X → Y is any function (not necessarily invertible), the preimage (or inverse image) of an element y ∈ Y is the set of all elements of X that map to y The ... set of all elements of X that map to S For example, take a function ƒ R → R, where ƒ x ↦ x2 ... This function is not invertible for reasons discussed above ...
Inverse Functions
... In mathematics, an inverse function is a function that undoes another function If an input x into the function ƒ produces an output y, then putting y into ... A function ƒ that has an inverse is called invertible the inverse function is then uniquely determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with exponentiation) ...

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