f(x-1/x)=x^3-1/x^3 则f(x)的解析式为?
问题描述：
f(x-1/x)=x^3-1/x^3 则f(x)的解析式为?
答
f(x-1/x)=x^3-1/x^3=(x-1/x)(x^2+1/x^2+1)=(x-1/x)[(x^2+1/x^2-2)+3]=(x-1/x)[(x-1/x)^2+3]则设x-1/x=T则f(T)=T*(T^2+3) =T^3+3T则f(x)=x^3+3x