The functions \(\mathrm f\) and \(\mathrm g\) are defined as follows, for all real values of \(x\).

\(\mathrm f(x)=2x^2-1\)

\(\mathrm g(x)=\mathrm e^x+1\)

(a) Solve the equation \(\mathrm{fg}(x)=8\).

(b) For each of the functions \(\mathrm f\) and \(\mathrm g\), either explain why the inverse function does not exist or find the inverse function, stating its domain.