f(x)=x(1/2^x-1+1/2)判断奇偶性

Question

如题所述

Answer 1

偶函数。
f(-x)=-x{1/[(2^-x)-1]+1/2}分式分子分母同乘2^x
=-x[2^x/(1-2^x)+1/2]系数-1带入括号
=x[2^x/(2^x-1)-1/2]分子-1再+1,然后把分式拆开
=x[1+1/(2^x-1)-1/2]化简
=x[1/(2^x-1)+1/2]
=f(x)