Definition:Root of a Function

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 $f$