A function f is defined by \(\mathrm{f}(x)=\mathrm{e}^{2 x+1}\) for \(x \in \mathbb{R}\). (a) State the range of \(\mathrm{f}^{-1}\). [1] (b) Find the domain of \(\mathrm{f}^{-1}\). [1] (c) Find an expression for \(\mathrm{f}^{-1}(x)\). [2] (d) 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. ![](https://cdn.mathpix.com/cropped/0ef1c1a8-20cf-4c74-8a6b-00c531bebfe2-09.jpg?height=1083&width=1268&top_left_y=366&top_left_x=400)

2026 - M/J - 0606/13 | Q8

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A function f is defined by \(\mathrm{f}(x)=\mathrm{e}^{2 ...