高考数学专题指数函数、对数函数、幂函数

高考数学专题复习指数函数对数函数、幂函数（理科）分

f(x)

x

(0≤

(0

(0

函

fx)(0x≤2)

东、理5给下三式

f(xy)(x)f(y，()(x)f(y)

f(y

f()f(y)1f(x)fy)

f()

x

f(x)sinx

f()logxf(x)tanx2依

f(x)f()f()

f(xyf(x)(y)

D

f(y

f()f(y)1f(x)fy)

∵

02

12

分

{Z2

{log2

(C)R

于

{Z|2

2

{Z|1{Z|x

{log2

{|

12

或x

(C)R

(C)R

从

2f(x)1

)

fx)

(

(0,1)

(

(U

22由

f(0)得xlg

11

1

0

分

f()f()x2)

2

f(xcos(x2)

fx

f(

(

(2

f(2)f(x)(

函

f()x

f(x

lg(|x

()

(

x2)f()||lg

|||

2lglg(1)|2

f()

f(xcos(x2)

f)x

2

log

x(0)

x

x

(2)

x

x

(x

x

x

(x

x

x

(x原(分a,c

2

log

c,

c

c

b

a

log12

10logb220log12

12

logccc12根

xx分

f()

11

M

x)x

NM

依

f()

11

{0}={

g(xln(1

N=

{|10}={|

{|{

本

12

且a观根分

f(x)

f(x)

11f()f)f)f()f()()323213f())f()f()f()f()333解

f(x)

y

f(x)

f(x)

f(x)

(

31f()f)2

131()f()f()f()f())333323

考

f

4,xxx

g2

函

f

xxx

g2

作

y

分

f(

x

g(x

2

f(x12

logx2

g(x

2

g(x

2

y

根f(x=[]

12

a

2

2

由

f(x)=logx[]

12

logloga

12=2

1

a

f(x

log

[a,2a]

y，xy

x0

x

y

f(x)alogx

ya

ylogx2

，函

f()a

log(0,

数问转f(xf(y)

f()a

log

x0

这

a

y

x

x

]

y

x|

1y

Ay0把文

yf)

y(

y

fx)

e0fx)3(e0

函

yf()

ylogxx3

y

f(

ylogxx3

f(x)3

x

R)

对

f

lg

且

4x

x且

考

y4log(1)(x2

反

(

9

x

0

xlog73

(3

x

2

x

03

x

或3

x

log73

四

f(x)

x

emf(x

[

f(x)

(x

t

f)

t

mf(

m

根aa根，D

a

f()loga

0

f(xf(x)(x12

i

332222in332222

f()()()1n

[解析

f(xf(f(xlogxx12aa1

f(x1

3

)f(

2

3

)(

n

3

)=logxa

logxa

3

loga

3

log(xxx)1

logxxa1

ylog2

C，向CC的。log(

ylog2

(2

C向，的

log(x2

a。由2

0

海。2

]时3>0

kkk

304

ya

0

ylog

x

0

x3y

1)2y22x•

y(x

2

[0,

在axalog

x

0a

yx

3y

R

y

112x

xx

•

)

2

y(x

2

[1,

y

江xaa0yy2yA。结x

•

。

y

0y

•

m

ym0

y

2

y

2

)

的

2

]x

]（x2

xy

2

log4

在N中且

y2

2

分可y|

2

m

]

y2|y

y

2

2|m

2a2a

0

2m

x1

x

2

x12

lg

10

y

y10

x

x1

y

y

20082008xyxyxx

y

y10

x

]

ya

2008x

,y11

y10c

x

yb

2008x

,2

y

,(,112

,y(,)11

yb

2008x

xx1

中，]]，

在

f(x)

a

11

(a0,a

f(x

f(x

f(xx]]

1x1x

(xx

f(x

(

f(x)f(

a

11log=1

f((x)

f(x

f()

log

a

11

222222x222222x

11

a0

1x1

0

x(0,1)

a

x

1f(x)()•logx

f(x

f

f(x)f(2)

]

1f(x)()•x

11f()()•logf()f(x)•logxxxx

1f()()•logf()f)•logxx

f()()•]•logxf)22

xlogx

f(x)

xlogx

f(2)

log

f(x)

xlogx

f(2)

f(x)

xx

(2)

x

x022

或x2

1x

fx)log()a

f(x

f(x

f

2)fx)

]

fx)log()

a

0

a

f(x

(

log(x)logaa