The function \(\mathrm{f}\) is defined by
where \(p\) is a real constant.
Find the range of \(\mathrm{f}\) if \(0\le p<9\).[1]
If \(p=6\),
find the exact solution(s) of \(\mathrm{f}(x)=4\),[2]
determine if \(\mathrm{f}\) has an inverse. Justify your answer.[1]
Find the inverse of \(\mathrm{f}\) in similar form when \(p=0\).[2]
The function \(\mathrm{g}(x)=18-3x\) for \(5\le x<6\). Explain why the composite function \(\mathrm{fg}\) exists and find its range.[3]