# A function and its inverse walked into a bar!

Calculus Level 4

Suppose a function $$f(x)$$ has an inverse, call it $$g(x)$$.

If $$f(3) = 4, f'(3) = \sqrt[3]{\dfrac{2}{5}}$$ and $$f''(3) = -\dfrac{4}{7}$$,

then $$g''(4) = \dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers.

Find $$a + b$$.

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