A simple corollary of Theorem SR: $f(x)=f_1(x) - f_2(x) =0$ if and only if $f_1(x)=f_2$.

For an elementary function, $f$ that can be expressed in a form with the final step in its definition being the difference of two elementary functions, $f_1$ and $f_2$, the corollary entails further that set of the roots of $f$ is the set of roots of the equation, $f_1(x)=g(x)$.

A mapping diagram can visualize these results by visually connecting coincident arrows in the mapping diagrams for $f_1$ and $f_2$ to a root of $f$.