Have You Tried The Simplest Substitution?

Algebra Level 4

\[ \left(f\left( x+y \right)\right)^2 \geq \left(f\left( x \right)\right)^2 + \left(f\left( y \right)\right)^2 \text{ for all } x, y \in\mathbb{R}.\]

Let \(f:\mathbb{R} \mapsto \mathbb{R}\) be a function that satisfy the condition above.

Evaluate \(f \left( 2016 \right) \).

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