Concept

Inverse function

Summary
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} . For a function f\colon X\to Y, its inverse f^{-1}\colon Y\to X admits an explicit description: it sends each element y\in Y to the unique element x\in X such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of f is the function f^{-1}\colon \R\to\R defined by f^{-1}(y) = \frac{y+7}{5} . Definitions Let f be a
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