Question

已知f(x^2-x)=x^4-2*x^3+x^2+1,则f(f(X))=_________

求详解啊~撒花

Answer 1

f(x^2-x)=x^4-2*x^3+x^2+1=x^2*(x^2-2x+1)+1=x^2*(x-1)^2+1=(x^2-x)^2+1
令t=x^2-x
则f(t)=t^2+1
f(x)=x^2+1
f(f(x))=(x^2+1)^2+1=x^4+2x^2+1+1=x^4+2x^2+2

Answer 2

f(x^2-x)=x^4-2*x^3+x^2+1=(x^2-x)^2+1
则f(x)=x^2+1
则f(f(x))=f(x)^2+1 =x^4+2x^2+2

Answer 3

f(x²-x)=x^4-2x³+x²+1=x^4-x³-(x³-x²)+1=x²(x²-x)-x(x²-x)+1
=(x²-x)²+1
所以，f(x)=x²+1；f[f(x)]=(x²+1)²+1

Answer 4

f(x²-x)=(x²-x)²+1
f(x)=x^2+1
f(f(x))=f(x+1)=x^4+2x^2+2