Satvik's Polynomial

Algebra Level 2

f(x)f(x) is a 5th5^\text{th}-degree polynomial such that f(1)=2,f(1)=2, f(2)=3,f(2)=3, f(3)=4,f(3)=4, f(4)=5,f(4)=5, f(5)=6,f(5)=6, and f(8)=7.f(8)=7.

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

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