Pöördfunktsiooniks

Pöördfunktsiooniks refers to the inverse function in mathematics. Given a function f, its inverse, denoted as f⁻¹, is a function that "reverses" the action of f. If f maps an element x from its domain to an element y in its codomain, then f⁻¹ maps y back to x. In other words, for any x in the domain of f, f⁻¹(f(x)) = x, and for any y in the domain of f⁻¹, f(f⁻¹(y)) = y.

For a function to have an inverse, it must be bijective, meaning it must be both injective (one-to-one) and surjective (onto). Injective means that each element in the codomain is mapped to by at most one element in the domain. Surjective means that each element in the codomain is mapped to by at least one element in the domain. If a function is not bijective, its domain or codomain may need to be restricted to make it bijective before an inverse can be defined.

The process of finding an inverse function often involves solving for the input variable in terms of the output variable. For example, if we have the function y = 2x + 1, to find the inverse, we would swap x and y to get x = 2y + 1 and then solve for y, resulting in y = (x - 1) / 2, which is the inverse function. The graphs of a function and its inverse are reflections of each other across the line y = x.