Segundo enunciado, podemos escrever:\begin{matrix} (h \circ f) &=& arctg \left(\dfrac{5+7^x}{4}\right) &=& \alpha \\ (h \circ g) &=& arctg \left(\dfrac{5-7^x}{4}\right) &=& \delta \end{matrix}Dado o comando, temos:\begin{matrix} (h \circ f)(a) &+& (h \circ f)(a) &=& \dfrac{\pi}{4} \\ \\ \alpha &+& \delta &=& 45^{\circ} \end{matrix}$\color{orangered}{Obs:}$ $\tan{(x+y)} = \dfrac{\tan{(x)} + \tan{(y)}}{1-\tan{(x)}\cdot \tan{(y)}}$ \begin{matrix} \tan{(\alpha + \delta)} = \tan{45^{\circ}} \\ \\ {{\dfrac{\tan{(\alpha)} + \tan{(\delta)}}{1-\tan{(\alpha)}\cdot \tan{(\delta)}} }}= 1 \\ \\ {\dfrac{5+7^a}{4} + \dfrac{5-7^a}{4} = {\normalsize{1}} - \dfrac{5+7^a}{4} \cdot \dfrac{5-7^a}{4} } \\ \\ 7^{2a} = 49 \\ \\ \fbox{$a = 1$} \end{matrix} Assim, \begin{matrix} f(a) - g(a) = {\dfrac{5+7^a}{4} - \dfrac{5-7^a}{4}} \\ \\ \fbox{$ f(a) - g(a) = \dfrac{7}{2}$} \\ \\ \\ Letra \ (D) \end{matrix}