Question

函数f(x)满足f(x^2+1)=x^4+5x^2-3,则f(x^2-1)=

Answer 1

令a=x^2+1则x^2=a-1x^2-1=a-2代入f(x^2+1)=x^4+5x^2-3f(a)=(a-1)^2+5(a-1)-3=a^2+3a-7f(x^2-1)=f(a-2)=(a-2)^2+3(a-2)-7=a^2-a-9=(x^2+1)^2-(x^2+1)-9所以f(x^2-1)=x^4+x^2-9