Continuous function/Squeeze criterion/Exercise

Let ${}a\in \mathbb {R}$ and let ${}f,g,h\colon \mathbb {R} \rightarrow \mathbb {R}$ be functions. Suppose that ${}g$ and ${}h$ are continuous in ${}a$, that ${}g(a)=f(a)=h(a)$ holds and suppose further that ${}g(x)\leq f(x)\leq h(x)$ holds for all ${}x\in \mathbb {R}$.

Show that also ${}f$ is continuous in ${}a$.

Create a solution