I’ve applied the glue rule to a question and found that $g(x)$, $f(x)$ and $h(x)$ are not equal at $x=2$. Does this mean that $f(x)$ is not continuous at $2$ for definite or do I now need to prove this further by another rule?
The glue rule I have been taught has been defined as;
Let $f$ be defined on the open interval $I$ and let $a$ be a member of $I$. If there are functions $g$ and $h$ such that
1) $f(x) = g(x)$, $x \in I$, $x \lt$ a
2) $f(x)=h(x)$,$x \in I$,$x \gt$ a
3)$f(a) = g(a) = h(a) $
4) $g$ and $h$ are continuous at $a$.
Then $f$ is continuous at $a$.