Let \(f\left( x \right) =\displaystyle \int _{ 2 }^{ x }{ \frac { dx }{ \sqrt { 1+{ x }^{ 4 } } } } \) and \( g \) be the inverse of \(f \). If \(g'\left( 0 \right) =n \) then find \( { n }^{ 2 } \).

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