若函数f(x)=log a (x+根号(bx^2+2a^2) ) (a>0且a不等于1)是奇函数,则实数对(a,b)=
问题描述:
若函数f(x)=log a (x+根号(bx^2+2a^2) ) (a>0且a不等于1)是奇函数,则实数对(a,b)=
答
若函数f(x)=log a (x+根号(bx^2+2a^2) ) (a>0且a不等于1)是奇函数-f(x)=f(-x)-log a (x+sqrt(bx^2+2a^2))=log a (-x+sqrt(bx^2+ax^2))1/ (x+sqrt(bx^2+2a^2)) =-x+sqrt(bx^2+ax^2)bx^2+2a^2-x^2=1(b-1)x^2=1-2a^2 ...