The function \(\mathrm{f}\) is given by
\(\mathrm{f}: x \mapsto \frac{4 - ax}{x + b}, \quad x \in \mathbb{R}, \quad x \neq -b,\)
where \(a\) and \(b\) are positive constants.
Sketch the graph of \(y = \mathrm{f}(x)\), stating the equations of any asymptotes and the coordinates of any points where the curve crosses the axes.[4]
Describe a sequence of \(3\) transformations that would transform the graph of \(y = \mathrm{f}(x)\) onto the graph of \(y = \frac{1}{x}\).[4]
Find \(\mathrm{f}^{-1}(x)\) and state its range.[3]
It is now given that \(b = a\).
Find the value of the composite function \(\mathrm{f}^{2025}(x)\) when \(x = 2\), giving your answer in terms of \(a\).[1]