設(shè)x<0,則-x>0,∵函數(shù)f(x)是R上的奇函數(shù),且當(dāng)x>0時(shí),f(x)=x
2-2x+1,
∴f(x)=-f(-x)=-[x
2-2(-x)+1]=-x
2-2x-1;
又f(0)=0;
∴f(x)在R上的表達(dá)式為f(x)=
| x2?2x+1,當(dāng)x>0時(shí) | 0,當(dāng)x=0時(shí) | ?x2?2x?1,當(dāng)x<0時(shí) |
| |
.
故答案為f(x)=
| x2?2x+1,當(dāng)x>0時(shí) | 0,當(dāng)x=0時(shí) | ?x2?2x?1,當(dāng)x<0時(shí) |
| |
.