1.對(duì)數(shù)函數(shù)的概念
一般地,函數(shù)y=logax(a>0,a≠1)叫做對(duì)數(shù)函數(shù),它的定義域是(0,+∞).
2.對(duì)數(shù)函數(shù)的圖象與性質(zhì)
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a>1
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0<a<1
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圖象
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性
質(zhì)
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定義域:(0,+∞)
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值域:R
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圖象過(guò)定點(diǎn)(1,0)
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在(0,+∞)上是單調(diào)增函數(shù)
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在(0,+∞)上是單調(diào)減函數(shù)
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3.反函數(shù)
對(duì)數(shù)函數(shù)y=logax(a>0且a≠1)和指數(shù)函數(shù)y=ax(a>0且a≠1)互為反函數(shù),它們的圖象關(guān)于y=x對(duì)稱(chēng).
一般地,如果函數(shù)y=f(x)存在反函數(shù),那么它的反函數(shù)記作y=f -1(x).
1.思考辨析(正確的打“√”,錯(cuò)誤的打“×”)
(1)對(duì)數(shù)函數(shù)的定義域?yàn)?b>R.( )
(2)y=log2x2與logx3都不是對(duì)數(shù)函數(shù). ( )
(3)對(duì)數(shù)函數(shù)的圖象一定在y軸右側(cè). ( )
(4)函數(shù)y=log2x與y=x2互為反函數(shù). ( )
[答案] (1)× (2)√ (3)√ (4)×
2.對(duì)數(shù)函數(shù)f(x)的圖象過(guò)點(diǎn)(4,2),則f(8)=________.
3 [設(shè)f(x)=loga x,則loga 4=2,∴a2=4,∴a=2,