已知f(x2+1）=x4+5x2-3,求f(x),f(x2-1)注：x2為X的平方

熱心網友

f(x2+1）=x4+5x2-3 =(X^4+X^2)+(4X^2+4)-7 =X^2(X^2+1)+4(X^2+1)-7 =X^2(X^2+1)+4(X^2+1)+4-11 =[(X^2+1)+2]^2-11所以f(x)=(X+2)^2-11故 f(X^2-1)=[(X^2-1)+2]^2-11 =(X^2+1)^2-11 =X^4+2X^2-10