已知对于f﹙x﹚有f﹙x+1﹚=3x³-4x²+5x-6,求f﹙x﹚

已知对于f﹙x﹚有f﹙x+1﹚=3x³-4x²+5x-6,求f﹙x﹚
已知对于f﹙x﹚有f﹙x+1﹚=3x³-4x²+5x-6,求f﹙x﹚

已知对于f﹙x﹚有f﹙x+1﹚=3x³-4x²+5x-6,求f﹙x﹚
f﹙x+1﹚=3x³-4x²+5x-6
令 t=x+1
则 x=t-1 代入
f(t)=3(t-1)³-4(t-1)²+5(t-1)-6
=3t³-9t²+9t-3-4(t²-2t+1)+5t-5-6
=3t³-9t²+9t-4t²+8t+5t-18
=3t³-13t²+22t-18
令t=x
则 f(x)=3x³-13x²+22x-18

以x＋1=t代入： 【x=t－1】
f(t)=3(t－1)³－4(t－1)²＋5(t－1)－6
f(t)=3t³－13t²＋22t－24
得：
f(x)=3x³－13x²＋22x－24

f﹙x+1﹚=3x³-4x²+5x-6
设t=x+1则x=t-1
f(t)=3(t-1)³-4(t-1)²+5(t-1)-6
=(t-1)[3(t-1) ²-4(t-1)+5]-6
=(t-1)[3t ²-10t+12]-6
=3t³-7t²+2t+6

f﹙x﹚=3x³-7x²+2x+6

f(x+1) = 3x^3-4x^2+5x-6
let y=x+1
f(y) = 3(y-1)^3-4(y-1)^2+5(y-1) -6
=3y^3-13y^2+22y-12
f(x) = 3x^3-13x^2+22x-12