A simple corollary of Theorem QU: For $f(x)=f_1(x) \div f_2(x)=\frac{f_1(x)}{f_2(x)}, f(x) = 1$ if and only if $f_1(x)=f_2(x)$.

For an elementary function, $f$ that can be expressed in a form with the final step in its definition being the quotient 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, $f_1(x)=f_2(x)$.

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 $f$.