Pöördarvfunktsioon

Pöördarvfunktsioon refers to the inverse function in mathematics. If a function f maps element x from set A to element y in set B, then the inverse function, denoted as f⁻¹, maps y back to x. This means that applying the function and then its inverse (or vice-versa) results in the original input. For example, if f(x) = 2x, then its inverse function f⁻¹(y) = y/2. Applying f to x gives 2x, and then applying f⁻¹ to 2x gives (2x)/2, which is x. Similarly, applying f⁻¹ to y gives y/2, and applying f to y/2 gives 2(y/2), which is y.

Not all functions have an inverse. A function must be bijective, meaning it must be both injective (one-to-one) and surjective (onto), to have a unique inverse. Injective means that each output has only one corresponding input. Surjective means that every element in the codomain is mapped to by at least one element in the domain. If a function is not bijective, its domain might need to be restricted to create a bijective sub-function for which an inverse can be defined. Common examples of functions with inverses include linear functions, exponential functions, and logarithmic functions. The concept of the inverse function is fundamental in many areas of mathematics, including calculus and algebra.