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

\(\mathrm f(x)=\frac{x+3}{x-1},\qquad \mathrm g(x)=1+x^2.\)

(a) Find \(\mathrm{fg}(x)\).

(b) Find \(\mathrm g^{-1}(x)\).

(c) Without using a calculator, solve the equation \(\mathrm f(x)=\mathrm g(x)\).