Inverse function

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An inverse function is a concept of mathematics. A function will calculate some output y, given some input x. This is usually written f(x) = y. The inverse function does the reverse. Let's say g() is the inverse function of f(), then g(y) = x . Or otherwise put, f(g(x)) = x. An inverse function to f(\ldots) is usually called f^{-1}(\ldots). Do not confuse f^{-1}(\ldots) with f(\ldots)^{-1}: the first is a value of an inverse function, the second is reciprocal of a value of a normal function.

Examples[change | change source]

Let's take a function f(x) = x^3 over real x. Then, f^{-1}(x) = \sqrt[3]{x}.

Not all functions have inverse functions: for example, function f(x) = |x| has none (because |-1| = 1 = |1|, and f^{-1}(x) should give both 1 and -1 when given 1)), but every binary relation has its own inverse relation.

Finding the inverse of a function can be very difficult to do.