The functions \(f\) and \(g\) are defined, for \(x\gt 1\), by

\(f(x)=9\sqrt{x-1}, \qquad g(x)=x^2+2.\)

(i) Find an expression for \(f^{-1}(x)\), stating its domain.

(ii) Find the exact value of \(fg(7)\).

(iii) Solve \(gf(x)=5x^2+83x-95\).