The figure below shows part of the graph of the function \(\mathrm{f}(x)=\dfrac{2x^2+3}{x^2-1}\).
Find the equations of all asymptotes of the curve \(C\).[2]
Find the range of the function.[2]
Find the corresponding point \(A^{\prime}\) of the y-intercept \(A\), under the transformation \(y=\mathrm{f}(3x-1)\).[2]
Determine whether \(\mathrm{f}(x)\) is even, odd or neither. Justify your answer.[2]
By using the graph above, or otherwise, solve the inequality \(\dfrac{2x^2+3}{x^2-1}>x-3\).[4]