The function \(\mathrm f\) is defined by \(\mathrm f(x)=-2x^2+9x-10\) for \(0\le x\le3\).
Write \(\mathrm f(x)\) in the form \(a+b(x+c)^2\) where \(a\), \(b\) and \(c\) are constants.[3]
Hence determine whether or not \(\mathrm f^{-1}\) exists.[2]
The function \(\mathrm g\) is defined by \(\mathrm g(x)=3\ln(5-2x)\) for \(0\le x<2.5\).
On the axes, sketch the graph of \(y=\mathrm g(x)\).
State the exact values of the intercepts with the coordinate axes and the equation of any asymptote.[3]
Find an expression for \(\mathrm g^{-1}(x)\).[2]
Find the domain and range of \(\mathrm g^{-1}\).
Give each of your answers in exact form.[2]