Too Hyperbolic?

Calculus Level 2

\[\large f\left( x \right) =\ln { \left(x+\sqrt { { x }^{ 2 }-1 }\right ) }, \quad x \ge 1 \]

For \(f\) as defined above, compute \( f\left(\sqrt { \dfrac { 1+\cosh { x } }{ 2 } }\right ) \).

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