函數(shù)f(x)=1+log 2 x(x≥2)的反函數(shù)f –1(x) = . 查看更多

 

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函數(shù)f(x)=1+log 2 x的反函數(shù)f –1(x)=           。

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若函數(shù)y=f(x)是函數(shù)y=ax-a(a>0,且a≠1)的反函數(shù),且f(
1
2
)=1,則函數(shù)y=(  )
A、log2x
B、
1
2x
C、log 
1
2
x
D、2x-2

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已知函數(shù)f(x)=log(x+)(a>1,x≥1).?

(1)求它的反函數(shù)f -1 (x),并指出f -1 (x)的定義域;

(2)當(dāng)1<a<2時(shí),證明f -1 (n)< (n∈N*).

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由函數(shù)y=f(x)確定數(shù)列{an},an=f(n),函數(shù)y=f(x)的反函數(shù)y="f" -1(x)能確定數(shù)列{bn},bn=" f" –1(n),若對(duì)于任意nÎN*,都有bn=an,則稱數(shù)列{bn}是數(shù)列{an}的“自反數(shù)列”.
(1)若函數(shù)f(x)=確定數(shù)列{an}的自反數(shù)列為{bn},求an;
(2)已知正數(shù)數(shù)列{cn}的前n項(xiàng)之和Sn=(cn+).寫出Sn表達(dá)式,并證明你的結(jié)論;
(3)在(1)和(2)的條件下,d1=2,當(dāng)n≥2時(shí),設(shè)dn=,Dn是數(shù)列{dn}的前n項(xiàng)之和,且Dn>log a (1-2a)恒成立,求a的取值范圍.

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由函數(shù)y=f(x)確定數(shù)列{an},an=f(n),函數(shù)y=f(x)的反函數(shù)y=f -1(x)能確定數(shù)列{bn},bn= f –1(n),若對(duì)于任意nÎN*,都有bn=an,則稱數(shù)列{bn}是數(shù)列{an}的“自反數(shù)列”.

   (1)若函數(shù)f(x)=確定數(shù)列{an}的自反數(shù)列為{bn},求an;

   (2)已知正數(shù)數(shù)列{cn}的前n項(xiàng)之和Sn=(cn+).寫出Sn表達(dá)式,并證明你的結(jié)論;

   (3)在(1)和(2)的條件下,d1=2,當(dāng)n≥2時(shí),設(shè)dn=,Dn是數(shù)列{dn}的前n項(xiàng)之和,且Dn>log a (1-2a)恒成立,求a的取值范圍.

 

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