\(f(x)=3e^{2x}+1\quad\text{for }x\in\mathbb{R}\)

\(g(x)=x+1\quad\text{for }x\in\mathbb{R}\)

(i) Write down the range of \(f\) and of \(g\).

(ii) Evaluate \(fg^2(0)\).

(iii) On the axes below, sketch the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\), stating the coordinates of the points where the graphs meet the coordinate axes.