已知,f(x-1)=x²+1,则f（x）=

已知,f(x-1)=x²+1,则f（x）=

,f(x-1)=x²+1,则f（x）=
令 x - 1 = k
x = k+1
,f(k)=x²+1 = ( k+1 )²+1 = k² +2k +1 + 1
= k² +2k + 2
f（x）=x² +2x + 2
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答：
f(x-1)=x²+1
=(x-1+1)²+1
=(x-1)²+2(x-1)+2
所以：
f(x)=x²+2x+2

f(x-1)=x*x-1+2=(x-1)(x-1+2)+2故f(x)=x(x+2)+2