A function \(\mathrm{f}\) is defined by \(\mathrm{f}(x)=e^{2x+1}\) for \(x\in\mathbb{R}\).
State the range of \(\mathrm{f}^{-1}\).[1]
Find the domain of \(\mathrm{f}^{-1}\).[1]
Find an expression for \(\mathrm{f}^{-1}(x)\).[2]
On the axes, sketch the graph of \(y=\mathrm{f}(x)\) and hence sketch the graph of \(y=\mathrm{f}^{-1}(x)\).
State the exact coordinates of any intercepts with the axes.[4]