Let $\displaystyle g$ be defined on $\displaystyle \mathbb{R}$ by $\displaystyle g(1) := 0$, and $\displaystyle g(x) := 2$ if $\displaystyle x \neq 1$, and let $\displaystyle f(x) := x +1$ for all $\displaystyle x \in \mathbb{R}$. How would you show that $\displaystyle \lim_{x\to0}g \circ f \neq (g \circ f)(0)$ ?