f(x)=loga [(1-mx)/(x-1)]是奇函数,求m

问题描述:

f(x)=loga [(1-mx)/(x-1)]是奇函数,求m
(a>0,a≠1)

因为 f(x)=loga(1-mx)/(x-1)是奇函数所以f(x)=-f(-x)loga (1-mx)/(x-1)+loga (1+mx)/(-x-1)=0(1-mx)*(1+mx)/(x-1)(-x-1)=11-m^2×x^2=1-x^2(m^2-1)x^2=0m1=1m2=-1m≠1所以:m=-1