The answer is not 11!

Algebra Level 4

Suppose f(x)f(x) is polynomial of degree 55 with leading coefficient of 2001. With f(1)=1f(1)=1, f(2)=3f(2)=3, f(3)=5f(3)=5, f(4)=7f(4)=7, f(5)=9f(5)=9. What is the value of f(6)f(6) ?

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