Sketch the graph of \(y=\dfrac{x+8}{x^2-3x+2}\), \(x\neq1,2\). Label clearly the equations of the asymptotes of the graph and the coordinates of all turning points and axial intercepts.[7]
Hence, solve the inequality \(\dfrac{(x+8)(x-2)}{x-1}\leq(x+8)(x-2)^2\).[5]
Consider the function \(\mathrm g:x\mapsto\dfrac{x+8}{x^2-3x+2}\), \(-8\leq x<1\).
Verify that \(\mathrm g^{-1}\) exists.[2]
Find \(\mathrm g^{-1}(12)\).[2]