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專題10函數(shù)的單調(diào)性和奇偶性綜合1.下列函數(shù)中,既是偶函數(shù)又在SKIPIF1<0上單調(diào)遞減的是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.已知奇函數(shù)SKIPIF1<0是定義在區(qū)間SKIPIF1<0上的增函數(shù),且SKIPIF1<0,則實數(shù)SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù),且在SKIPIF1<0上單調(diào)遞減,SKIPIF1<0,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.設(shè)SKIPIF1<0是奇函數(shù),且在SKIPIF1<0上是減函數(shù),SKIPIF1<0,則SKIPIF1<0的解集是(
)A.SKIPIF1<0或SKIPIF1<0 B.SKIPIF1<0或SKIPIF1<0C.SKIPIF1<0或SKIPIF1<0 D.SKIPIF1<0或SKIPIF1<05.若函數(shù)SKIPIF1<0,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06.定義在R上的偶函數(shù)SKIPIF1<0滿足:對任意的SKIPIF1<0,有SKIPIF1<0.則當(dāng)SKIPIF1<0時,有(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<07.已知函數(shù)SKIPIF1<0,若實數(shù)a滿足SKIPIF1<0,則a的取值范圍(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知偶函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù),若SKIPIF1<0,則SKIPIF1<0的大小關(guān)系為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<09.已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,SKIPIF1<0是偶函數(shù),SKIPIF1<0,SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010.已知奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,SKIPIF1<0,則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<011.若SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù),對SKIPIF1<0,當(dāng)SKIPIF1<0時,都有SKIPIF1<0,則SKIPIF1<0,SKIPIF1<0,SKIPIF1<0的大小關(guān)系是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<012.定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0,當(dāng)SKIPIF1<0時,SKIPIF1<0,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<013.已知對于任意的SKIPIF1<0,都有SKIPIF1<0成立,且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<014.已知函數(shù)f(x)是定義在R上的奇函數(shù),若對任意的SKIPIF1<0,且SKIPIF1<0,都有SKIPIF1<0成立,則不等式SKIPIF1<0的解集為(
)A.(SKIPIF1<0,1) B.(-∞,1) C.SKIPIF1<0 D.SKIPIF1<015.已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù),若對于任意SKIPIF1<0,不等式SKIPIF1<0恒成立,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<016.若SKIPIF1<0在定義域內(nèi)的任意SKIPIF1<0都滿足SKIPIF1<0,則稱SKIPIF1<0為奇函數(shù),可知奇函數(shù)的圖象關(guān)于原點中心對稱;若SKIPIF1<0在定義域內(nèi)的任意SKIPIF1<0都滿足SKIPIF1<0,則SKIPIF1<0稱為偶函數(shù),可知偶函數(shù)的圖象關(guān)于SKIPIF1<0軸對稱.知道了這些知識現(xiàn)在我們來研究如下問題:已知函數(shù)SKIPIF1<0,SKIPIF1<0是定義在SKIPIF1<0上的函數(shù),且SKIPIF1<0是奇函數(shù),SKIPIF1<0是偶函數(shù),SKIPIF1<0,若對于任意SKIPIF1<0,都有SKIPIF1<0,則實數(shù)SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<017.已知函數(shù)SKIPIF1<0,則關(guān)于SKIPIF1<0不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<018.已知函數(shù)SKIPIF1<0,SKIPIF1<0,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<019.已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足:函數(shù)SKIPIF1<0為奇函數(shù),且當(dāng)SKIPIF1<0時,SKIPIF1<0成立(SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)),若SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,則SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的大小關(guān)系是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<020.已知SKIPIF1<0為定義在SKIPIF1<0上的偶函數(shù),SKIPIF1<0,且當(dāng)SKIPIF1<0時,SKIPIF1<0單調(diào)遞增,則不等式SKIPIF1<0的解集為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<021.(多選)已知奇函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的減函數(shù),且SKIPIF1<0,若SKIPIF1<0,則下列結(jié)論一定成立的是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<022.SKIPIF1<0是定義在R上的奇函數(shù),且滿足以下兩個條件:SKIPIF1<0對任意的SKIPIF1<0SKIPIF1<0都有SKIPIF1<0;SKIPIF1<0當(dāng)SKIPIF1<0時,SKIPIF1<0,且,則函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值為__________.23.若函數(shù)SKIPIF1<0為奇函數(shù),則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為______.24.已知函數(shù)SKIPIF1<0,SKIPIF1<0,若SKIPIF1<0,則實數(shù)SKIPIF1<0的取值范圍是______.25.若函數(shù)SKIPIF1<0,則不等式SKIPIF1<0的解集為______.26.已知函數(shù)SKIPIF1<0是定義在R上的偶函數(shù),對任意m,SKIPIF1<0都有SKIPIF1<0,且SKIPIF1<0.若SKIPIF1<0,則實數(shù)a的取值范圍是______.27.已知SKIPIF1<0,若SKIPIF1<0恒成立,則實數(shù)SKIPIF1<0的取值范圍___.28.已知函數(shù)SKIPIF1<0的定義域SKIPIF1<0,且對任意SKIPIF1<0,恒有SKIPIF1<0,當(dāng)SKIPIF1<0時,SKIPIF1<0,若SKIPIF1<0,則m的取值范圍為__________.29.已知函數(shù)SKIPIF1<0為SKIPIF1<0上的偶函數(shù),當(dāng)SKIPIF1<0時,SKIPIF1<0.(1)求SKIPIF1<0時,SKIPIF1<0的解析式;(2)寫出函數(shù)SKIPIF1<0的單調(diào)增區(qū)間;(3)若SKIPIF1<0,求SKIPIF1<0的取值范圍.30.已知函數(shù)SKIPIF1<0為R上的奇函數(shù).(1)求SKIPIF1<0的值,并用定義證明函數(shù)SKIPIF1<0的單調(diào)性;(2)求不等式SKIPIF1<0的解集;(3)設(shè)SKIPIF1<0,若對任意的SKIPIF
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