f(x)=loga(x+根号下x方+2a方)是奇函数则实数a=
问题描述：
f(x)=loga(x+根号下x方+2a方)是奇函数则实数a=
答
f(-x)=loga[-x+√(x^2+2a^2)]
=-f(x)=-loga[x+√(x^2+2a^2)]
=loga{1/[x+√(x^2+2a^2)]}
所以-x+√(x^2+2a^2)=1/[x+√(x^2+2a^2)]
所以[x+√(x^2+2a^2)][-x+√(x^2+2a^2)]=1
所以x^2+2a^2-x^2=1
a^2=1/2
a是底数大于0
a=√2/2