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Question Number 170994 by Mastermind last updated on 05/Jun/22

$$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{function}\mathrm{h}\left(\mathrm{x}\right)={\mathrm{x}}^5-2\mathrm{x}$$$$\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{function}$$$$$$$$\mathrm{Mastermind}$$

Answered by Rasheed.Sindhi last updated on 06/Jun/22

$$\mathrm{h}\left(\mathrm{x}\right)={\mathrm{x}}^5-2\mathrm{x}$$$$\mathrm{h}(-\mathrm{x})={(-\mathrm{x})}^5-2(-\mathrm{x})$$$$=-{\mathrm{x}}^5+2\mathrm{x}$$$$=-({\mathrm{x}}^5-2\mathrm{x})$$$$=-\mathrm{h}\left(\mathrm{x}\right)$$$$\therefore \mathrm{h}\left(\mathrm{x}\right)\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{function}.$$

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