The function \(\mathrm{f}\) is defined by
Sketch the graph of \(y=\mathrm{f}(x)\), giving the equations of the asymptotes and the coordinates of the axial intercepts. Hence show that \(\mathrm{f}\) is a one-one function.[3]
The diagram below shows the graph of \(y=\mathrm{g}(x)\). The curve cuts the axes at \(\left(0,\frac{1}{2}\right)\) and \((1,0)\), and also
passes through \((2,-3)\). It has asymptotes \(y=-6\) and \(y=6\).
Find the value of \(\mathrm{g}\mathrm{f}^{-1}(6)\).[3]
Explain why the function \(\mathrm{fg}\) does not exist.[1]
Another function \(\mathrm{h}\) is defined by
On separate diagrams, sketch the graphs of
\(y=\mathrm{h}(x)\),[3]
\(y=\mathrm{h}^{-1}(x)\),[3]
stating the equations of the asymptotes and the coordinates of any axial intercept.
Describe the relationship between the graphs of \(y=\mathrm{h}(x)\) and \(y=\mathrm{h}^{-1}(x)\).[1]