Question

Given $f(x)=\frac{-2x^{2}14x-12}{x-1}.$

Which of the following statements about the continuity of $f(x)$ at $x=-2$ are true?

Select the correct answer below:

$f(x)$ is not continuous at $x=-2$ because it is not defined at $x=-2.$

$f(-2)$ exists, but $f(x)$ is not continuous at $x=-2$ because $\underset{x-2}{lim}f(x)$ does not exist.

$f(-2)$ and $\underset{x-2}{lim}f(x)$ both exist, but $f(x)$ is not continuous at $x=-2$ because $\underset{x-2}{lim}f(x)f(-2).$

$f(x)$ is continuous at $x=-2.$

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