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let be a function so

$ f(x)= x^{2}+h(x) $ , here $h(x) $ is a function so $ h(x) = O(logx)$

it is clear that $ f(x) \sim x^{2} $ for big 'x' so the inverse

$ f^{-1}(x)\sim x^{1/2}$ for big 'x' is this correct, does this mean that the function $ f(x)$ has an inverse and that this inverse will be asymptotic to $ x^{1/2} $ ?

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    You have to specify the the $x$-domain you have in mind.2012-07-11

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