f1(x)f^{-1}(x) Does not means 1f(x)\frac{1}{f(x)}

Calculus Level 2

Let f:RRf:\mathbb{R}\rightarrow \mathbb{R} be defined by f(x)=x3+3x+1f(x) = x^3+3x+1 and gg be the inverse of ff. If the value of g(5)g''(5) is equal to ab\dfrac{-a}{b}, where aa and bb are coprime positive integers, find the value of a+ba+b.

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