Given that the maximum value is \(5\), find \(p\) and the range of \(f\).[2]
Give a full geometric description of the transformation from \(y=\cos x\) to \(y=f(x)\).[2]
Sketch the graph of \(f\) for \(0\le x\le\pi\).[2]
Solve \(f(x)<2\) for \(0\le x\le\pi\).[2]
Find the values of \(k\) for which \(f(x)=k\), \(0\le x\le\pi\), has
exactly three solutions;
no solutions.[2]
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Answer:(a) \(p=2\), range \([-1,5]\). (d) \([0,\frac{\pi}{8})\cup(\frac{3\pi}{8},\frac{5\pi}{8})\cup(\frac{7\pi}{8},\pi]\). (e) (i) \(k=-1\); (ii) \(k<-1\) or \(k>5\).