The function f is defined by \(\mathrm{f}(x)=2 x-1\) for \(x \in \mathbb{R}\). (a) Explain why the function \(\mathrm{f}^{2}\) can be formed.

(b) On the axes, sketch the graph of \(y=\left|\mathrm{f}^{2}(x)\right|\).

State any intercepts with the coordinate axes.

(c) It is given that \(\left|\mathrm{f}^{2}(x)\right| \leqslant a x+b\) for \(-1 \leqslant x \leqslant 3\) and for no other values of \(x\).

Find the values of \(a\) and \(b\).