$• \ \text{Afirmativa I:}$ $\color{orangered}{\text{Falsa}}$ \begin{matrix} (f \circ g) \ (x) = m.(x+m) + 1 \\ (g \circ f) \ (x) = m.(x+1) + 1 \\ \\ m.(x+m) + 1 = m.(x+1) + 1 \\ m = 1 \\ \color{gray}{\fbox{$0<m<1$}} \end{matrix}$• \ \text{Afirmativa II:}$ $\color{orangered}{\text{Falsa}}$ \begin{matrix} \begin{cases}f(m) = m^2 + 1 \\ g(m) = 2m\end{cases}&\therefore& m^2 + 1 \ne 2m \end{matrix}$• \ \text{Afirmativa III:}$ $\color{orangered}{\text{Falsa}}$ \begin{matrix} \begin{cases}(f \circ g) \ (a) &=& m(a+m) + 1 \\ f(a) &=& ma + 1 \end{cases} &\Rightarrow& m=0 &,& \color{gray}{\fbox{$0<m<1$}} \end{matrix}$• \ \text{Afirmativa IV:}$ $\color{orangered}{\text{Falsa}}$ \begin{matrix} (f \circ g) \ (b) = m(b+m) + 1 \\ \\ m(b+m) + 1 = mb \\ m^2 = -1 \end{matrix}$• \ \text{Afirmativa V:}$ $\color{#3368b8}{\text{Verdadeira}}$\begin{matrix} (g\circ g) \ (m) = (m +m) + m \\ \\ 0<m<1 \\ 0<3m< 3 \\ \\ 0<(g\circ g) \ (m) < 3 \\ \\ Letra \ (E) \end{matrix}