1. $f(x)=3{e}^{2x}+1$ for $x\inℝ$ $g(x)=x+1$ for $x\inℝ$

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

(ii) Find${g}^{2}(0)$.

(iii) Hence find ${fg}^{2}(0)$ .

(iv) On the axes below, sketch the graphs of $y=f(x)$ and $y={f}^{–1}(x)$ . State the intercepts with the coordinate axes and the equations of any asymptotes.