# Nth Root Function

## Nth Root Function

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

### Examples

• Consider the function defined by the relationship $$f(x) = {x^2}$$. 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 :

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