How can I obtain the inverse of the function below analytically?
$$e^{(0.0116t^2-0.4212t)},\ \ \ 0<t \leq 7.0633$$
Someone insists that it can be analytically obtained.
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Welcome to math.SE: in order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. – mlc Mar 28 '17 at 12:08
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Let: $$y=e^{0.0116t^2-0.4212t}$$ Then, taking logarithms on both sides: $$\ln{y}=0.0116t^2-0.4212t$$ Therefore: $$0.0116t^2-0.4212t-\ln{y}=0$$ Note that you can now use the quadratic formula to solve explicitly for $t$.
projectilemotion
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1I don't why I never thought to use quadratic formula there. Thank you :) – YONGSEEN KIM Mar 29 '17 at 12:01