反函數(shù)競賽試題及答案一、單項選擇題（每題2分，共40分）1.函數(shù)f(x)=2x+3的反函數(shù)是？A.f?1(x)=x/2-3B.f?1(x)=(x-3)/2C.f?1(x)=x/2+3D.f?1(x)=(x+3)/22.若函數(shù)f(x)=x3+1，則其反函數(shù)f?1(x)的表達(dá)式為？A.f?1(x)=?(x-1)

B.f?1(x)=?x-1

C.f?1(x)=(x-1)3

D.f?1(x)=x3-13.函數(shù)f(x)=e?的反函數(shù)是？A.f?1(x)=lnxB.f?1(x)=e?C.f?1(x)=1/xD.f?1(x)=x24.函數(shù)f(x)=log?x的反函數(shù)是？A.f?1(x)=2?B.f?1(x)=x2C.f?1(x)=log?2D.f?1(x)=1/log?x5.若f(x)=3x-5的反函數(shù)為f?1(x)，則f?1(4)的值為？A.3B.1/3

C.9D.-16.函數(shù)f(x)=(x+2)/(x-1)的反函數(shù)是？A.f?1(x)=(x+2)/(x-1)B.f?1(x)=(x+1)/(x-2)C.f?1(x)=(2x+1)/(x-1)D.f?1(x)=(x+1)/(2-x)7.下列哪個函數(shù)的反函數(shù)是其本身？A.f(x)=xB.f(x)=x2

C.f(x)=1/x

D.f(x)=-x8.若函數(shù)f(x)=ax+b（a≠0）的反函數(shù)為f?1(x)，則f?1(x)的斜率為？A.1/a

B.-aC.aD.-1/a9.函數(shù)f(x)=sinx在區(qū)間[-π/2,π/2]上的反函數(shù)是？A.f?1(x)=arcsinx

B.f?1(x)=arccosx

C.f?1(x)=tanxD.f?1(x)=cotx10.函數(shù)f(x)=cosx在區(qū)間[0,π]上的反函數(shù)是？A.f?1(x)=arccosxB.f?1(x)=arcsinxC.f?1(x)=secxD.f?1(x)=cscx11.函數(shù)f(x)=tanx在區(qū)間(-π/2,π/2)上的反函數(shù)是？A.f?1(x)=arctanx

B.f?1(x)=arccotx

C.f?1(x)=sinxD.f?1(x)=cosx12.若f(x)=2?的反函數(shù)為f?1(x)，則f?1(8)的值為？A.2

B.3

C.4

D.513.函數(shù)f(x)=x2（x≥0）的反函數(shù)是？A.f?1(x)=√xB.f?1(x)=-√xC.f?1(x)=x2D.f?1(x)=1/x14.函數(shù)f(x)=1/(x+1)的反函數(shù)是？A.f?1(x)=1/x-1B.f?1(x)=(1-x)/x

C.f?1(x)=x/(1-x)

D.f?1(x)=1/(x-1)15.若f(x)=ln(x+1)的反函數(shù)為f?1(x)，則f?1(0)的值為？A.0

B.1C.eD.e-116.函數(shù)f(x)=x3的反函數(shù)是？A.f?1(x)=?xB.f?1(x)=x^(1/3)C.f?1(x)=x3D.f?1(x)=1/x317.函數(shù)f(x)=2x/(x+1)的反函數(shù)是？A.f?1(x)=x/(2-x)B.f?1(x)=(2x)/(1-x)C.f?1(x)=x/(x-2)D.f?1(x)=(1-x)/(2x)18.若f(x)=e^(2x)的反函數(shù)為f?1(x)，則f?1(e2)的值為？A.1

B.2C.1/2

D.019.函數(shù)f(x)=log?x的反函數(shù)是？A.f?1(x)=3?B.f?1(x)=x3C.f?1(x)=log?3D.f?1(x)=1/log?x20.函數(shù)f(x)=(x-1)/(x+1)的反函數(shù)是？A.f?1(x)=(1+x)/(1-x)B.f?1(x)=(x-1)/(x+1)C.f?1(x)=(1-x)/(1+x)D.f?1(x)=(x+1)/(x-1)二、多項選擇題（每題2分，共40分）1.下列哪些函數(shù)存在反函數(shù)？A.f(x)=x2B.f(x)=x3C.f(x)=|x|D.f(x)=e?2.函數(shù)f(x)=ax+b（a≠0）的反函數(shù)具有哪些性質(zhì)？A.斜率為1/aB.與原函數(shù)關(guān)于y=x對稱C.截距為-b/aD.定義域與原函數(shù)值域相同3.下列哪些函數(shù)的反函數(shù)是其本身（考慮定義域）？A.f(x)=xB.f(x)=1/x（x≠0）C.f(x)=-x

D.f(x)=x34.關(guān)于反函數(shù)，下列說法正確的是？A.原函數(shù)單調(diào)則反函數(shù)存在B.反函數(shù)的定義域是原函數(shù)的值域C.反函數(shù)的值域是原函數(shù)的定義域D.所有函數(shù)都有反函數(shù)5.下列哪些函數(shù)的反函數(shù)可以通過交換x和y并解出y得到？A.f(x)=2x+1B.f(x)=x2+1（x≥0）C.f(x)=sinx（x∈[-π/2,π/2]）D.f(x)=1/x（x≠0）6.若f(x)的反函數(shù)為f?1(x)，則下列哪些等式成立？A.f(f?1(x))=x

B.f?1(f(x))=x

C.f(x)·f?1(x)=1

D.f(x)+f?1(x)=07.下列哪些函數(shù)的反函數(shù)是奇函數(shù)？A.f(x)=x3B.f(x)=e?C.f(x)=lnx

D.f(x)=x8.關(guān)于反函數(shù)的圖像，下列說法正確的是？A.與原函數(shù)圖像關(guān)于y=x對稱B.與原函數(shù)圖像完全相同C.與原函數(shù)圖像沒有交點D.反函數(shù)圖像的存在性取決于原函數(shù)的單調(diào)性9.下列哪些函數(shù)的反函數(shù)可以通過對數(shù)運(yùn)算得到？A.f(x)=e?

B.f(x)=2?

C.f(x)=log?x

D.f(x)=x210.若f(x)是雙射函數(shù)，則下列哪些說法正確？A.f(x)存在反函數(shù)B.f(x)的反函數(shù)唯一C.f(x)的反函數(shù)也是雙射函數(shù)D.f(x)的反函數(shù)定義域與原函數(shù)相同三、判斷題（每題1分，共10分）1.所有函數(shù)都有反函數(shù)。（）2.函數(shù)f(x)=x2的反函數(shù)是f?1(x)=±√x。（）3.若f(x)是單調(diào)函數(shù)，則f(x)一定存在反函數(shù)。（）4.反函數(shù)的定義域是原函數(shù)的定義域。（）5.函數(shù)f(x)=e?的反函數(shù)是f?1(x)=lnx。（）6.若f(x)和g(x)互為反函數(shù)，則f(g(x))=x且g(f(x))=x。（）7.函數(shù)f(x)=1/x的反函數(shù)是其本身。（）8.反函數(shù)的圖像與原函數(shù)的圖像關(guān)于x軸對稱。（）9.若f(x)是奇函數(shù)，則其反函數(shù)也是奇函數(shù)。（）10.函數(shù)f(x)=sinx在R上的反函數(shù)是f?1(x)=arcsinx。（）四、填空題（每題1分，共10分）1.函數(shù)f(x)=3x-2的反函數(shù)是f?1(x)=______。2.函數(shù)f(x)=log?x的反函數(shù)是f?1(x)=______。3.若f(x)=2?的反函數(shù)為f?1(x)，則f?1(4)=______。4.函數(shù)f(x)=(x+1)/(x-1)的反函數(shù)是f?1(x)=______。5.函數(shù)f(x)=x3+1的反函數(shù)是f?1(x)=______。6.若f(x)和g(x)互為反函數(shù)，則f(g(2))=______。7.函數(shù)f(x)=e^(x+1)的反函數(shù)是f?1(x)=______。8.函數(shù)f(x)=√x（x≥0）的反函數(shù)是f?1(x)=______。9.若f(x)=ln(x-1)的反函數(shù)為f?1(x)，則f?1(0)=______。10.函數(shù)f(x)=tanx在區(qū)間(-π/2,π/2)上的反函數(shù)是f?1(x)=______。

答案：一、單項選擇題1.B2.A3.A4.A5.A6.B7.A8.A9.A10.A11.A12.B13.A14.B15.A16.A17.A18.A19.A20.A二、多項選擇題1.BD2.ABCD3.AB4.