The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined by
Without finding the inverse function of \(\mathrm{f}\), find the exact value of \(\mathrm{f}^{-1}(1)\).[2]
On the same diagram, sketch the graphs of \(y=\mathrm{g}(x)\) and \(y=\mathrm{g}^{-1}(x)\), showing clearly the relationship between them. Give the equations of any asymptotes and the coordinates of any points where the graphs cross the \(x\)- and \(y\)-axes.[3]
Without finding the inverse function of \(\mathrm{g}\), solve \(\mathrm{g}^{-1}(x)=\mathrm{g}(x)\), giving your answer to 3 significant figures.[2]
Determine if the composite function \(\mathrm{gf}\) exists.[2]