Chapter 2.1, Problem 41E

Consider $f$ and $g$ two functions defined on the same set of real numbers $D$ . Let $\text{a}=\langle x,f\left(x\right)\rangle$ and $\text{b}=\langle x,g\left(x\right)\rangle$ be two vectors that describe the graphs of the functions, where $x\in D.$ Show that if the graphs of the functions $f$ and $g$ do not intersect, then the vectors $\text{a}$ and $\text{b}$ are not equivalent.