Logic

Algebra Level 3

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

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