Logic

Algebra Level 3

Given:f(x)=x2f\left( x \right) =\frac { x }{ \sqrt { 2 } } , g(x)=f(x)2+x2g\left( x \right) ={ f\left( x \right) }^{ 2 }+{ x }^{ 2 } and f(x)f(x)f(x)f(x)...=2\huge{ f\left( x \right) }^{ { { f\left( x \right) }^{ { f\left( x \right) }^{ f\left( x \right) } } }^{ ... } }=2

What is the value of g(x)g\left( x \right) ?

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