# The Hidden Function

Algebra Level 3

$\begin{cases} g(x) = x^2 - 11x + 30 \\ g(f(x)) = x^4 - 14x^3 + 62x^2 - 91x + 42 \end{cases}$

Let $$g$$ and $$f$$ be the monic polynomial functions that satisfy the system above. What is the value of $$f(7)$$?

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