Determine where the following function is discontinuous 

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 $x=\frac{4}{3}$.