问题
填空题
已知f(x+1)=2x2+1,则f(x-1)=______.
答案
设x+1=t,则x=t-1,
f(t)=2(t-1)2+1=2t2-4t+3,
f(x-1)=2(x-1)2-4(x-1)+3
=2x2-4x+2-4x+4+3
=2x2-8x+9.
故答案:2x2-8x+9.
已知f(x+1)=2x2+1,则f(x-1)=______.
设x+1=t,则x=t-1,
f(t)=2(t-1)2+1=2t2-4t+3,
f(x-1)=2(x-1)2-4(x-1)+3
=2x2-4x+2-4x+4+3
=2x2-8x+9.
故答案:2x2-8x+9.