Question: Let

\[g\left( x \right)=\left\{ \begin{aligned} & \frac{{{x}^{2}}-6x+8}{{{x}^{2}}-5x+6}\,\,\,\,\,\,\,\,\,x>2 \\ & 2x-2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\le x<2 \\ & -2x+2\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<0 \\ \end{aligned} \right.\]

(a) Show that \(g\left( x \right)\) is continuous on the interval [5, 8].

(b) Find all points of discontinuity for \(g\left( x \right)\).