Wortelfunctie

Wortelfunctie refers to the inverse function of a power function. Specifically, if a function is defined as y = x^n, then its corresponding wortelfunctie is x = y^(1/n), which is also known as the n-th root of y. For example, the wortelfunctie of y = x^2 is x = y^(1/2) or x = sqrt(y). Similarly, the wortelfunctie of y = x^3 is x = y^(1/3) or x = cube_root(y).

The domain and range of a wortelfunctie are often related to those of the original power function, but with the roles of domain and range reversed. For instance, if the original function is defined for all real numbers, its wortelfunctie might have restrictions depending on whether n is even or odd. When n is even, the wortelfunctie typically requires a non-negative input to produce a real output, especially when considering the principal root.

The graphical representation of a wortelfunctie is a reflection of the original power function across the line y = x. This geometric property highlights the inverse relationship between the two functions. Understanding wortelfuncties is crucial in various mathematical contexts, including solving equations, analyzing growth and decay models, and in calculus for differentiation and integration. They are fundamental building blocks in algebra and pre-calculus.