An algebra problem by Priyanshu Mishra

Algebra Level 5

Let \(f: \mathbb R \rightarrow \mathbb R\) for all reals \(x, y\) such that

\[\large f( x+y ) + f( x )f( y ) = f( x ) + f( y ) + f( xy ) .\]

If only one non-constant function exists satisfying above relation, find \(f(2017) \).

Notation: \(\mathbb R \) denotes the set of real numbers.


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