Question

设F（x）=(1+2/ex-1)*F(x)(x≠0)是偶数函数,且f(x)不恒等于零,试判断f(x)是奇数函数还是偶数子

Answer 1

F（x）=(1+2/ex-1)*f(x)=[(e^x+1)/(e^x-1)]*f(x)

F(-x)=[(e^-x+1)/(e^-x-1)]*f(-x)

=[(1+e^x)/(1-e^x)]*f(-x)

=[(1+e^x)/(e^x-1)]* -f(-x)

F(x)是偶函数 ,F(X)=F(-X)

[(e^x+1)/(e^x-1)]*f(x) =[(1+e^x)/(e^x-1)]* -f(-x) f(x)=-f(-x)

所以f(x)为奇函数