"Root of an equation" vs "Root of a function"

Question

I realize that various sources do not differentiate the use of the word root for both equations and functions. Should their usage need a revision? I other words, shouldn't we use just zeros of a function instead of the roots of a function? And, keep roots for just equations.

Answer 1

A root of a function $f$ is a solution $x$ to the equation $$ f(x) = 0. $$ For instance, $\pi$ is a root of the equation $x\sin x=0$. (See this article from Encyclopedia Britannica.)

For $g, h$, the root of an equation $$ g(x) = h(x) \tag{1} \label{e} $$ is the $x$ such that the equation (\ref{e}) is true. Observe that we can define $$ j(x) = g(x) - h(x) $$ such that the root of $j$ is also the root of equation (\ref{e}).