The function \(\mathrm f\) is defined by \(\mathrm f(x)=(x-2)^2\), \(-1\leq x<2\).
On the axes below, sketch the graph of \(\mathrm f\), indicating clearly the coordinates of the end points.[2]
On the same axes below, sketch the graph of \(\mathrm f^{-1}\), showing clearly the geometrical relationship between \(\mathrm f\) and \(\mathrm f^{-1}\).[2]
The function \(\mathrm g\) is defined by \(\mathrm g(x)=\mathrm e^{x-2}\), \(x\in\mathbb R\).
Explain why the function \(\mathrm f\circ\mathrm g\) cannot be defined over the entire set of real numbers.[2]