Write \(2x^2-2x+3\) in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are constants.[3]
It is given that \(\mathrm{f}(x)=2x^2-2x+3\), for \(x\le p\).
Write down the greatest value of \(p\) for which \(\mathrm{f}\) has an inverse.[1]
Using this value of \(p\), write down the range of \(\mathrm{f}\).[1]
Using this value of \(p\), find an expression for \(\mathrm{f}^{-1}\).[3]