Continuous functions/f(x) bigger g(x)/Neighborhood/Exercise

Let ${}a\in \mathbb {R}$ and let

$f,g\colon \mathbb {R} \longrightarrow \mathbb {R}$

be continuous functions with

${}f(a)>g(a)\,.$

Show that there exists some ${}\delta >0$ such that

${}f(x)>g(x)\,$

holds for all ${}x\in [a-\delta ,a+\delta ]$.

Create a solution