Based on the IMO

Algebra Level 5

\[f\left( x+a \right) \le af\left( x \right) +f\left( f\left( x \right) \right) \]

A function \(f\left( x \right)\) is defined for all real numbers \(x\) and returns a real number for every input \(x\) (That is, \(f: \mathbb R\rightarrow \mathbb R\)). The above describes this function, where \(a\) is a real number. What is the value of \(f\left( -1 \right) \)?


This problem is based on an IMO problem from a few years back.
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