證明：
定義域 x≠0,關(guān)于原點(diǎn)對(duì)稱.
f(x)=x(1/(2^x-1)+1/2))+a
f(-x)=-x*{1/[2^(-x)-1]+1/2)}+a
=-x*{2^x/(1-2^x)+1/2}+a
=-x[(2^x-1+1)/(1-2^x)+1/2]+a
=-x[-1+1/(1-2^x)+1/2]+a
=-x[1/(1-2^x)-1/2]+a
=x*[1/(2^x-1)+1/2]+a
=f(x)
所以 f(x)是偶函數(shù)