ümberpööramisfunktsioon

ümberpööramisfunktsioon is an Estonian term that translates to "inversion function" or "inverse function" in English. It refers to a fundamental concept in mathematics where for a given function, its ümberpööramisfunktsioon "undoes" the operation performed by the original function. If a function f maps an input x to an output y (f(x) = y), then its ümberpööramisfunktsioon, often denoted as f⁻¹, maps the output y back to the original input x (f⁻¹(y) = x).

For an ümberpööramisfunktsioon to exist, the original function must be bijective, meaning it must be both injective (one-to-one) and surjective (onto). Injective means that each output value corresponds to a unique input value, and surjective means that every possible output value in the codomain is actually achieved by the function.

Common examples include arithmetic operations. The ümberpööramisfunktsioon of addition is subtraction, and the ümberpööramisfunktsioon of multiplication is division. In calculus, the ümberpööramisfunktsioon of differentiation is integration, and vice versa. Understanding ümberpööramisfunktsioonid is crucial for solving equations, simplifying expressions, and exploring various mathematical relationships. It allows for the reversal of transformations and the recovery of original values.