f（x）=loga（a的2x次方+1）-x
f(-x)= loga（a的-2x次方+1）+x
= loga（(1+a的2x次方)/(a的2x次方)+x
= loga（(1+a的2x次方)-loga (a的2x次方)+x
=loga（(1+a的2x次方)-2x+x
=loga（(1+a的2x次方)-x=f(x)
f(x)是偶函数