Functions are awesome!!!

Algebra Level 4

Find the number of functions \( f : \mathbb{R} \rightarrow \mathbb{R} \) such that \[f(x+y)=f(x)\cdot f(y)\cdot f(xy)\] for all \(x,y\) in \( \mathbb{R} \).

Note: \( \mathbb{R}\) denotes the set of real numbers.

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