Sketching an inverse sine function with a cosine curve, their intersection and the range of the cosine function

The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined for \(-1\le x\le1\) by \(\mathrm{f}(x)=\arcsin x+\dfrac{x}{2}\) and \(\mathrm{g}(x)=2\cos2x\).

1. Using the grid provided, draw sketches of the curves \(y=\mathrm{f}(x)\) and \(y=\mathrm{g}(x)\).[4]
2. Write down the \(x\)-coordinate of the point where the two curves meet.[1]
3. Write down the set of values taken by \(\mathrm{g}(x)\).[1]