f(x)=1/(2的x次方-1)+1/2
f(x)=[2+2的x次方-1]/[2*(2的x次方-1)]
=[1+2的x次方]/[2*(2的x次方-1)]
f(-x)=1/(2的-x次方-1)+1/2
=2的x次方/[1-2的x次方]+1/2
=[2*2的x次方+1-2的x次方]/{2*[1-2的x次方]}
=[1+2的x次方]/{2*[1-2的x次方]}
=-[1+2的x次方]/[2*(2的x次方-1)]
=-f(-x)
所以为奇函数!
f(x)=1/(2^x-1)+1/2
f(x)=[2+2^x-1]/[2*(2^x-1)]
=[1+2^x]/[2*(2^x-1)]
f(-x)=1/[2^(-x)-1]+1/2
=2^x/[1-2^x]+1/2
=[2*2^x+1-2^x]/{2*[1-2^x]}
=[1+2^x]/{2*[1-2^x]}
=-[1+2^x]/[2*(2^x-1)]
=-f(-x)
所以为奇函数!