Question Number 40116 by maxmathsup by imad last updated on 15/Jul/18
$${let}\:{f}\left({x}\right)\:=\:\frac{{e}^{{x}^{\mathrm{2}} } −\mathrm{1}}{{x}}\:\:{if}\:{x}\neq\mathrm{0}\:\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${prove}\:{that}\:\:{f}^{−\mathrm{1}} \left({x}\right)={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{2}}\:+{o}\left({x}^{\mathrm{3}} \right)\:\:\:\left({x}\rightarrow\mathrm{0}\right) \\ $$