A piecewise function \( f(x) \) is defined as follows:
\[ f(x) =
  \begin{cases} 
   2x + 3 & \text{if } x \leq 1 \\
   x^2 - 1 & \text{if } x > 1
  \end{cases}
\]
Another function \( g(x) = 3x - 4 \). Determine \( f(g(x)) \) and find the value of \( f(g(2)) \). Let's think step by step and output the final answer within \boxed{}.
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