Question

若f(x)=a-(2/(2^x+1))是奇函数 求实数a的值

Answer 1

∵f(x)=a-2/(1+2^x)是奇函数

∴必须满足f(-x)=-f(x)

即a-2/(1+2^(-x))=-a+2/(1+2^x)

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

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

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

故a=1.