wortelfuncties

Wortelfuncties, also known as radical functions, are mathematical functions that involve taking a root of a variable. The most common type of root is the square root, represented by the symbol $\sqrt{}$. A square root function has the general form $f(x) = \sqrt{x}$. This function takes a non-negative number $x$ and returns its principal (non-negative) square root. The domain of $f(x) = \sqrt{x}$ is all real numbers greater than or equal to zero, i.e., $[0, \infty)$. The range is also $[0, \infty)$.

Other types of wortelfuncties include cube root functions, such as $g(x) = \sqrt[3]{x}$, which involves taking the third root of a variable. Unlike square root functions, cube root functions can accept negative inputs, as every real number has a real cube root. The domain and range of $g(x) = \sqrt[3]{x}$ are both all real numbers, i.e., $(-\infty, \infty)$. In general, an $n$-th root function can be written as $h(x) = \sqrt[n]{x}$ or $h(x) = x^{1/n}$. When $n$ is an even integer, the domain is restricted to non-negative real numbers. When $n$ is an odd integer, the domain includes all real numbers.

Wortelfuncties are essential in various areas of mathematics, including algebra, calculus, and trigonometry. They are used to solve equations, model real-world phenomena involving growth or decay, and understand relationships between different quantities. Transformations of wortelfuncties, such as translations, stretches, and reflections, can alter their graphs and properties, leading to a wide variety of related functions.