令 x+1=t 则 x=t-1代入
f(t) = (t-1)^2 + 2(t-1) + 3
= t^2 -2t + 1 + 2t - 2 + 3
=t^2 + 2
所以f(x) = x^2 + 2
f(x)=x^2+2
设t=x+1 则f(t)=(t-1)^2+2(t-1)+3整理得f(t)=t^2+2,把t换成x,则f(x)=x^2+2
f(x+1)=(x+1-1)^2+2(x+1-1)+3替x+1为x得:
f(x)=(x-1)^2+2(x-1)+3整理得:
f(x)=x^2+2
f(x+1)=(x+1)^2+2
f(x)=x^2+2