若對一切實(shí)數(shù)x總有f(10+x)=f(10-x)且f(20+x)=-f(20-x)求證函數(shù)y=f(x)的圖象關(guān)于原點(diǎn)對稱.

熱心網(wǎng)友

函數(shù)圖象關(guān)于原點(diǎn)對稱即y=f(x)為奇函數(shù).證明:f(-x)=f(10+(-10-x)=f(10-(-10-x))=f(20+x)=-f(20-x)=-f(10+(10-x))=-f(10-(10-x))=-f(x),所以y=f(x)為奇函數(shù),即函數(shù)y=f(x)的圖象關(guān)于原點(diǎn)對稱.

熱心網(wǎng)友

f(-x)=f(10+(-10-x)=f(10-(-10-x))=f(20+x)=-f(20-x)=-f(10+(10-x))=-f(10-(10-x))=-f(x)