Let $a$ be a positive real number. The functions f and g are defined on the set of real numbers as
$$\begin{aligned}
& f(x) = x + a \\
& g(x) = ax + 1
\end{aligned}$$
Given that $(\mathbf{f} \cdot \mathbf{g})(\mathbf{1}) = (\mathbf{f} + \mathbf{g})(\mathbf{2})$, what is $\mathbf{g}(\mathbf{7})$?
A) 8
B) 15
C) 22
D) 29
E) 36