Both linear functions whose composite with a given quadratic equals a stated quadratic

The functions \(\mathrm{f}\) and \(\mathrm{g}\), each with domain \(\mathbb{R}\), are given by \(\mathrm{f}(x)=ax+b\) and \(\mathrm{g}(x)=x^2-3x+1\), where \(a\) and \(b\) are integers.

It is known that \((\mathrm{g}\circ\mathrm{f})(x)=9x^2+3x-1\) for all \(x\). Find both possible expressions for \(\mathrm{f}(x)\).[7]