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I need to simplify function $g(x)$ which I describe below.

Let $F(y)$ be the inverse of $f'(\cdot)$ i.e. $F = \left( f'\right)^{-1}$ and $f(x): \mathbb{R} \to \mathbb{R}$, then $$g(x) =\int_a^x F(y)dy$$ Is it possible to simplify $g(x)$?

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    By "inversion" do you mean the inverse, $(f')^{-1}(x)$, or the reciprocal, $\frac{1}{f'(x)}$?2012-06-04
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    thank you for question. I meant the inverse $(f')^{-1}(x)$2012-06-04

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