The function \(\mathrm{f}\) is defined by \(\mathrm{f}(x)=2x^2-6x+4\) for all real values of \(x\).
Write \(\mathrm{f}(x)\) in the form \(a(x+b)^2+c\) where \(a\), \(b\) and \(c\) are constants.[3]
Hence find the range of \(\mathrm{f}\).[1]
The function \(\mathrm{g}\) is defined by \(\mathrm{g}(x)=2x^2-6x+4\) for \(x\le k\), where \(k\) is a constant.
Given that \(\mathrm{g}\) has an inverse, state the largest possible value of \(k\).[1]
The function \(\mathrm{h}\) is defined by \(\mathrm{h}(x)=e^{3x}-1\) for \(x\le0\).
Given that \(\mathrm{gh}(x)\) exists, find \(\mathrm{gh}(x)\), simplifying your answer.[3]