$Determine where the following function is discontinuous$

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$Determine where the following function is discontinuous$

Determine where the following function is discontinuous

$$f(x)=\frac{x^2-9}{3x^2+2x-8}.$$

Calculus Continuity Domain

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The function $f$ is discontinuous when there is division by zero. Lets find the points where the denominator is zero
\[3x^2+2x-8=0 \Rightarrow x=\frac{-2\pm \sqrt{4-4\times 3 \times (-8)}}{2 \times 3}=\frac{-2\pm \sqrt{100}}{2 \times 3} \]
\[=\frac{-2\pm10}{6}=-2, \frac{8}{6}.\]
Thus the function $f$ is discontinuous at $x=-2$ and $x=\frac{4}{3}$.

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$Determine where the following function is discontinuous$

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