Definition:Root of Mapping

Definition
Let $$f: R \to R$$ be a function on a ring $$R$$.

Let $$x \in R$$.

Then the values of $$x$$ for which $$f \left({x}\right) = 0_R$$ are known as the roots of the function $$f$$.

This is simply a generalization of the case where $f$ is a polynomial.

Zero of a Function
The field $$K$$ is usually the set of real numbers $$\R$$ or complex numbers $$\C$$.

In this case, for a given function $$f$$, the roots are often called the zeroes of the function $$f$$