The function \(\mathrm{f}\) is defined by

\(\mathrm{f}(x)=x^2+2x-3,\qquad x\geq -1.\)

(a) Explain why \(\mathrm{f}^{-1}\) exists.

(b) On the same axes, sketch the graphs of \(y=\mathrm{f}(x)\) and \(y=\mathrm{f}^{-1}(x)\), giving the coordinates of the vertex of each graph and the intercepts on the coordinate axes.