2020 SJI P2 Q4

Let \(\mathrm{f}\) and \(\mathrm{g}\) be the following functions

\[\mathrm{f}(x)=x^4+0.2x^3-5.8x^2-x+4,\quad 0\leq x\leq p,\]

\[\mathrm{g}(x)=-3+2\sin(x-1),\quad-\frac\pi2+1\leq x\leq\frac\pi2+1.\]

1. Find the largest value of \(p\) in 3 significant figures for which \(\mathrm{f}\) has an inverse.[2]
2. Solve the equation \(\mathrm{f}^{-1}(x)=1\).[2]
3. Hence, solve \((\mathrm{f}^{-1}\circ\mathrm{g})(x)=1\).[3]