A calculus problem by Brilliant Member

Calculus Level 3

\[f(x)=-4\sqrt { { e }^{ 1-{ x } } } +1+{ x }+\frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 3 } }{ 3 } \]

If \(g(x)\) is the inverse of \(f(x)\) above, then find \(\dfrac 2 {g' \left(\frac {-7}6\right)}\), where \(g'\) is the first derivative of \(g\).

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