Period, range, sketch, equation, inequality and number of roots for a transformed cosine function

The function \(\mathrm{f}\) is defined by \(\mathrm{f}(x)=2\cos4x+3\) for \(0\le x\le\frac{5\pi}{8}\).

1. For the function \(\mathrm{f}\), find[3]
   1. its period;
   2. its range.
2. On the axes provided below, sketch the graph of \(y=\mathrm{f}(x)\).[4]
3. Find all solutions of the equation \(\mathrm{f}(x)=4\).[2]
4. Solve the inequality \(\mathrm{f}(x)\ge3\).[3]
5. Given that the equation \(\mathrm{f}(x)=k\) has exactly two roots in the domain of \(\mathrm{f}\), find all possible values of \(k\).[2]