Question

对于函数f(x)=a-2/(2的x次方+1)(a属于R),是否存在实数a使函数为奇函数?

Answer 1

若函数f(x)为奇函数

f(-x)=-f(x)即:

a-2/(2^(-x)+1)=-a+2/(2^x+1)

整理为:

2a=2/(2^(-x)+1)+2/(2^x+1)

a=1/(2^(-x)+1)+1/(2^x+1)

=2^x/(2^x+1)+1/(2^x+1)

=(2^x+1)/(2^x+1)

=1