The diagram shows the graph of $$\(y=\mathrm{f}(x)\)$$, where $$\(\mathrm{f}(x)=\frac{3}{2} \cos 2 x+\frac{1}{2}\)$$ for $$\(0 \leqslant x \leqslant \pi\)$$. A function $$\(\mathrm{g}\)$$ is such that $$\(\mathrm{g}(x)=\mathrm{f}(x)+k\)$$, where $$\(k\)$$ is a positive constant. The $$\(x\)$$-axis is a tangent to the curve $$\(y=\mathrm{g}(x)\)$$. State the value of $$\(k\)$$ and hence describe fully the transformation that maps the curve $$\(y=\mathrm{f}(x)\)$$ on to $$\(y=\mathrm{g}(x)\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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