A function $f(x)$ is said to have a removable discontinuity at $x=a$ if both of the following conditions hold:

1. $f$ is either not defined or not continuous at $x=a$.
   
   
2. $f(a)$ could either be defined or redefined so that the new function is continuous at $x=a$.

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Show that $$f(x) = \begin{cases}\displaystyle{x^{2}+8x+21}&\text{if}\ x < -4\cr \displaystyle{-2}&\text{if}\ x = -4\cr \displaystyle{-x^{2}-8x-11}&\text{if}\ x > -4\end{cases}$$ has a removable discontinuity at $x=-4$ by

(a) verifying (1) in the definition above, and then

(b) verifying (2) in the definition above by determining a value of $f(-4)$ that would make $f$ continuous at $x=-4$.

$f(-4)=$ would make $f$ continuous at $x=-4$.

Now draw a graph of $f(x)$. It's just a couple of parabolas!