Nth Root Function

Function defined by a relationship of the form f(x) = [latex]\sqrt[n]{x}[/latex], where x ∈ [latex]\mathbb{R}_{+}[/latex], if n is even and not equal to zero, or x ∈ [latex]\mathbb{R}[/latex] if n is odd.

Examples

Consider the function defined by the relationship [latex]f(x) = {x^2}[/latex]. The graph of f is shown below, as is the graph of the reciprocal relation of f (dashed line), which can be divided into two to form the graphs of the functions g and h which are two square root functions :

racine n-ieme

Consider the function defined by the relationship [latex]f(x) = {x^3}[/latex]; in this case, it can be noted that the reciprocal of the function is also a function and corresponds to the cube root function [latex]g\left ( x \right )=\sqrt[3]{x}[/latex] :

racine cubique