函数f(x)满足关系式 (x-1)f[(x+1)/(x-1)]-f(x) = x ,其中 x 不等于1 ,求 f(x)的表达式.
热心网友
解:设:(x+1)/(x-1)=T === x=(T+1)/(T-1)x-1=2/T[2/(T-1)]*f(T)-f[(T+1)/(T-1)=(T+1)/(T-1)2f(T)-(T-1)f[(T+1)/(T-1)]=T+1因为:(x-1)f[(x+1)/(x-1)]-f(x)=x让:x=T(T-1)f[(T+1)/(T-1)-f(T)=T...........(1)-(T-1)f[(T+1)/(T-1)]+2f(T)=T+1......(2)(1)+(2)f(T)=2T+1所以:f(x)=2x+1