Question Number 5234 by sanusihammed last updated on 02/May/16
$${Show}\:{that}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:.\:\:\mid{x}\mid\:\:=\:\:{odd} \\ $$
Answered by prakash jain last updated on 02/May/16
$${a}.\:{x}\geqslant\mathrm{0} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \centerdot{x}={x}^{\mathrm{3}} \\ $$$${f}\left(−{x}\right)={x}^{\mathrm{2}} \left(−{x}\right)=−{x}^{\mathrm{3}} \\ $$$$ \\ $$$${b}.\:{x}<\mathrm{0} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \left(−{x}\right)=−{x}^{\mathrm{3}} \\ $$$${f}\left(−{x}\right)={x}^{\mathrm{2}} \centerdot{x}={x}^{\mathrm{3}} \\ $$$$ \\ $$$${f}\left({x}\right)=−{f}\left({x}\right) \\ $$$$ \\ $$