Two routes to the same answer

Algebra Level 3

Let (x+3)(x+1)f(x)=(x+2)(x+4)f(x1)(x+3)(x+1)f(x)=(x+2)(x+4)f(x-1) be true for all real xx and that f(3)=f(2)+22f(3)=f(2)+22.

Find f(4)f(4).

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