哥哥姐姐帮忙写下过程好吗谢了若F(x)是奇函数,则函数G(x)=F(x)[1/(e^x+1)-1/2]的图象关于对称.

Question

哥哥姐姐帮忙写下过程好吗谢了
若 F(x) 是奇函数,则函数G(x)=F(x)[1/(e^x+1)-1/2] 的图象关于_________对 称.

Answer 1

G(x)=F(x)[1/(e^x+1)-1/2]
G(-x)=F(-x)[1/(e^（-x）+1)-1/2] =-F(x)[e^x/(e^x+1)-1/2] =-F(x)[（e^x-1）/2(e^x+1)]
=-F(x)[（e^x+1-2）/2(e^x+1)]=F(x)[1/(e^x+1)-1/2] =G(x)
故为偶函数