A function \(f\) is defined, for \(x\leqslant \dfrac32\), by \(f(x)=2x^2-6x+5\).

(i) Express \(f(x)\) in the form \(a(x-b)^2+c\), where \(a\), \(b\) and \(c\) are constants.

(ii) On the same axes, sketch the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\), showing the geometrical relationship between them.

(iii) Using your answer from part (i), find an expression for \(f^{-1}(x)\), stating its domain.