f(x+1/x)=x2+1/x2,g(x+1/x)=x3+1/x3,求f(g(x))

问题描述:

f(x+1/x)=x2+1/x2,g(x+1/x)=x3+1/x3,求f(g(x))

f(x+1/x)=x^2+1/x^2=(x+1/x)^2-2
so f(x)=x^2-2
g(x+1/x)=x^3+1/x^3=(x+1/x)^3-3(x+1/x)
so g(x)=x^3-3x
so f(g(x))=(x^3-3x)^2-2=x^6-6x^4+9x^2-2