我们将具有下列性质的所有函数组成集合M:函数y=f(x)(x∈D),对任意
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均满足
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,当且仅当x=y时等号成立.
(1)若定义在(0,+∞)上的函数f(x)∈M,试比较f(3)+f(5)与2f(4)大小.
(2)设函数g(x)=-x
2,求证:g(x)∈M.
(3)已知函数f(x)=log
2x∈M.试利用此结论解决下列问题:若实数m、n满足2
m+2
n=1,求m+n的最大值.
考点分析:
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如图所示,南山上原有一条笔直的山路BC,现在又新架设了一条索道AC.小李在山脚B处看索道AC,发现张角∠ABC=120°;从B处攀登400米到达D处,回头看索道AC,发现张角∠ADC=160°;从D处再攀登800米方到达C处.问索道AC长多少(精确到米)?
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记函数f(x)=
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的定义域为A,g(x)=log
3[(x-m-2)(x-m)]的定义域为B.
(1)求A;
(2)若A⊆B,求实数m的取值范围.
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在直三棱柱ABC-A
1B
1C
1中,已知AB=AC=AA
1=4,∠BAC=90°,D为B
1C
1的中点,求异面直线AB
1与CD所成角的大小.
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将1,2,…,9这9个数平均分成三组,则每组的三个数都可以成等差数列的概率为( )
A.
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B.
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C.
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D.
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设向量
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=(-2,1),
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=(1,λ) (λ∈R),若
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、
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的夹角为135°,则λ的值是( )
A.3
B.-3
C.3或-
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D.-3或
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