A Problem I Found In A Paper Bag Made Out Of A Mathematics Question Paper

Algebra Level 3

For the function f:RRf: \mathbb {R\to R}, if f(2x)f(x)=xf(2x) - f(x) = x for all real xx and f(0)=1f(0) = 1, then find the value of f(2)f(2).

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