f(x)=-2x+(a/2)x+1+b
(1)当x=1时f(x)=-2x+2-x-1+1=-2x+2-x/2+1
f(-x)+f(x)=-2-x+2x/2+1+-2x+2-x/2+1=-2x/2+3/2×2x+2≠0,即f(-x)≠-f(x)
所以当a=b=1时f(x)不为奇函数.
(2)当f(x)为奇函数时必满足f(-x)=-f(x),即f(-x)+f(x)=0
f(-x)+f(x)= (-2-x+(a/2)-x+1+b)+( -2x+(a/2)x+1+b)=(ax+1/2-1)2-x +( a1-x/2-1)2x +2b=0
解之可得a=2,b=-1