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Inverse Function ○꠹｜Definition｜1st｜20260511170638-00-⌔

Inverse function - Wikipedia

Inverse function

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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 $f:X\to Y$, its inverse $f^{-1}:Y\to X$ 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) = 5 x − 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 output, then divides the result by 5. Therefore, the inverse of f is the function $f^{-1}:\mathbb{R}\to \mathbb{R}$ defined by $f^{-1}(y)=\frac{y+7}{5}.$

Printed 2026-06-28.

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