Satvik's Polynomial

Algebra Level 3

\(f(x)\) is a \(5^\text{th}\) degree polynomial such that \(f(1)=2,\) \(f(2)=3,\) \(f(3)=4,\) \(f(4)=5,\) \(f(5)=6,\) and \(f(8)=7.\)

If the value of \(f(9)\) can be expressed as \(\dfrac{a}{b}\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

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