7. What comedians have in common with the players in a
comedy is their way of playing with words.
6. Acting our stereotypes of people from different countries
can be very funny.
5. Much of the wisdom discovered by early Chinese
scientists is still useful for farming.
4. Not only is food production important but also taking
care of the environment.
3. To make as much use of the land as possible, two or
more crops are planted each year where possible.
2. It is on this arable land that the farmers produce food
for the whole population of China.
1. What do you think causes these changes?
12.(16分)已知函数f(x)=x2-4ax+2a+6(a∈R).
(1)若函数的值域为[0,+∞),求a的值;
(2)若函数值为非负数,求函数f(a)=2-a|a+3|的值域.
[解析] (1)∵函数的值域为[0,+∞),
∴Δ=16a2-4(2a+6)=0,
即2a2-a-3=0,得a=-1或a=.
(2)∵对一切x∈R函数值均为非负,
∴Δ=8(2a2-a-3)≤0⇒-1≤a≤,
∴a+3>0,
∴f(a)=2-a|a+3|
=-a2-3a+2
=-2+,
11.(15分)已知函数f(x)=-xm,且f(4)=-.
(1)求m的值;
(2)判断f(x)在(0,+∞)上的单调性,并给予证明.
[解析] (1)f(4)=-,∴-4m=-,m=1.
(2)f(x)=-x在(0,+∞)上单调递减.
现证之:任取x1、x2∈(0,+∞)且x1<x2,则x2-x1>0,
∴f(x2)-f(x1)=-
=(x1-x2).
∵x2-x1>0,x1x2>0,∴f(x2)-f(x1)<0.
∴f(x)=-x,在(0,+∞)上单调递减.
10.(15分)已知函数y=-x2+ax-+在区间[0,1)上的最大值是2,求实数a的值.
[解析] y=-2+(a2-a+2),对称轴为x=.
(1)当0≤≤1即0≤a≤2时,ymax=(a2-a+2),由(a2-a+2)=2得a=3或a=-2,与0≤a≤2矛盾,不合要求.
(2)当<0即a<0时,y在[0,1]上单调减,有ymax=f(0),由f(0)=2⇒-+=2⇒a=-6.
(3)当>1即a>2时,y在[0,1]上单调增,有ymax=f(1),由f(1)=2⇒-1+a-+=2⇒a=
综上,得a=-6或a=.
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