A curve has equation $$\(y=3 \cos 2 x+2\)$$ for $$\(0 \leqslant x \leqslant \pi\)$$. Functions $$\(\mathrm{f}, \mathrm{g}\)$$ and $$\(\mathrm{h}\)$$ are defined for $$\(x \in \mathbb{R}\)$$ by $$\[ \begin{aligned} & \mathrm{f}(x)=3 \cos 2 x+2, \\ & \mathrm{~g}(x)=\mathrm{f}(2 x)+4, \\ & \mathrm{~h}(x)=2 \mathrm{f}\left(x+\frac{1}{2} \pi\right) . \end{aligned} \]$$  Describe fully a sequence of transformations that maps the graph of $$\(y=\mathrm{f}(x)\)$$ on to $$\(y=\mathrm{h}(x)\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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