G(X)=F(X)×loga[x+√(x²+1)],F(x)=F(-x)
G(-x)=F(-x)×loga[-x+√(x²+1)]=F(x)×loga[-x+√(x²+1)]
那么G(x)+G(-x)=F(x)×{loga[x+√(x²+1)]+loga[-x+√(x²+1)]}
=F(x)×loga{[x+√(x²+1)][-x+√(x²+1)]}
=F(x)×loga[(x²+1)-x²]
=F(x)×loga1
=0
那么G(x)=-G(-x),所以G(x)是奇函數(shù),那么G(x)的圖象關(guān)于原點(diǎn)對稱