Question

已知f(x+1)=x^2-3x+2，求f(x)和f(x-1)的解析式．

Answer 1

f(x)就把f（x+1）中右边的x换成x-1
f（x-1）就把f（x+1）中右边的x换成x-2

Answer 2

f(x)=(x-1)^2-3(x-1)+2
=x^2-2x+1-3x+3+2
=x^2-5x+6

f(x-1)=(x-1)^2-5(x-1)+6
=x^2-2x+1-5x+5+6
=x^2-7x+12

Answer 3

f(x+1)=(x+1)^2-5(x+1)+6
所以f(x)=x^2-5x+6
f(x-1)=(x-1)^2-5(x-1)+6=x^2-7x+12

Answer 4

1. 设x+1=y,then x=y-1, f(y)=(y-1)(y-1)-3(y-1)+2=y^2-2y+1-3y+3+2=y^2-5y+6, so f(x)=x^2-5x+6

2. set x=t-1, then f(t-1)=(t-1)^2-5(t-1)+6=t^2-2t+1-5t+5+6=t^2-7t+12, so f(x-1)=x^2-7x+12