问题 填空题

设函数f(x)=mx2-mx-6+m.若对于m∈[-2,2],f(x)<0恒成立,则实数x的取值范围是______.

答案

函数可整理为f(x)=(x2-x+1)m-6

∵对于m∈[-2,2],f(x)<0恒成立,

∴(x2-x+1)m-6<0恒成立.

令g(m)=(x2-x+1)m-6

则函数g(m)在区间[-2,2]上的最大值小于0,

∵g(m)为一次函数,且一次项系数x2-x+1=(x-

1
2
)2+
3
4
>0

∴函数g(m)在区间[-2,2]上单调递增,

[g(m)]max=g(2)=2x2-2x-4

∴2x2-2x-4<0

解得-1<x<2

故正确答案为:(-1,2)

单项选择题

I was a single parent of four small children, working at a low paid job. Money was always tight, but we had a (1) over our heads, food on the table, clothes on our backs, and if not a lot, always (2) . Not knowing we were poor, my kids just thought I was (3) . I’ve always been glad about that.

It was Christmas time, and although there wasn’t (4) for a lot of gifts, we planned to celebrate with a family party. But the big (5) for the kids was the fun of Christmas (6) .

They planned weeks ahead of time, asking (7) what they wanted for Christmas. Fortunately, I had saved MYM120 for (8) to share by all five of us.

The big (9) arrived. I gave each kid a twenty-dollar bill and (10) them to look for gifts of about four dollars each. Then everyone scattered. We had two hours to shop; then we would (11) back at the "Santa’s Workshop"

Driving home, everyone was in high Christmas spirits, (12) my younger daughter, Ginger, who was unusually (13) She had only one small, flat bag with a few candies—fiftycent candies I was so angry, but I didn’t say anything (14) we got home. I called her into my bedroom and closed the door, (15) to be angry again. This is what she told me.

"I was looking (16) thinking of what to buy, and I (17) to read the little cards on the ’Giving Trees’. One was for a little girl, four years old, and all she (18) for Christmas was a doll. So I took the card off the tree and (19) the doll for her. We have so much and she doesn’t have anything. "

I never felt so (20) as I did that day.

10()。

A.shopping 

B.travelling 

C.parties 

D.greetings

单项选择题