Quite large

Algebra Level 4

Let \(f(x) = 9x+2\) and \(g(x) = 25x+6 \). Find the sum of all possible constant terms of all functions that are compositions of the functions \(f\) and \(g\) in which \(f\) and \(g\) each appear exactly 4 times.

For example, a composition of \(f\) and \(g\) in which \(f\) and \(g\) each appear exactly 2 times could be \(f(f(g(g(x))))\) or \(f(g(f(g(x))))\).

Also note that the constant term of a function \(h\) is equal to \(h(0) \).

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