Consider two functions \( f(x) = 3x + 2 \) and \( g(x) = \frac{x - 2}{3} \). Verify that \( g(x) \) is the inverse function of \( f(x) \). Then, if \( f(a) = 17 \), find \( a \) and \( g(f(a)) \). Let's think step by step and output the final answer within \boxed{}.
user