组卷网>知识点选题>利用奇偶性求函数解析式
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1 . 已知函数fx)=axa>0,a≠1)的图象经过点eqId536793918db741f0b87251bdcdf81d91.
(1)函数fx)=gx)+hx),其中gx)为奇函数,hx)为偶函数,求hx),gx)的解析式;
(2)x∈(0,1]时,2lnhx)-lngx)-t=0有解,求实数t的取值范围.
2 . 已知eqId9657e4d1fe3647c2a2fc0f9301f2ab8f分别是定义在R上的奇函数和偶函数,且eqId39a05fb933784b829fca75e71046ba69,则eqIdcc188b103a23424b90006800cd8df432(   )
A.8B.-8C.16D.-16
3 . eqId144eff5c0e4649138a21f2b1b6a06907是定义在R上的奇函数,且当eqId26126945e23544d9b0cecaf9cf4809ac时,eqId9b8a246d2a4648d4b761edef0ed6905f
(1)求eqId4db620a5946b4ee0a9f530f35a6d505a时,eqId6f13759e937144069819aed2ae5a1057的解析式;
(2)求eqId144eff5c0e4649138a21f2b1b6a06907的单调减区间.
4 . 已知eqId6f13759e937144069819aed2ae5a1057是定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数,且当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqIdc849966698b946dfb67f33df021d9c55,则eqId1d3844067a2d4ce783612c376a627daa的值为(   )
A.eqId4adf22999d4e47da945bc7c62e3f9824B.eqId96c7406fe9bb42d482404e87ed3f58bdC.eqId3b29afc35d5a4bdfab8a0674ec37b12dD.3
5 . 函数eqId6f13759e937144069819aed2ae5a1057eqId7dcd2312d0bf4bb1befdfcc170e45791上为奇函数,当eqIdaa1312dcc8e24925b421f7767761a363时,eqId857bb5e85ed8444a84a58c21bfd0fbe4,则当eqId4db620a5946b4ee0a9f530f35a6d505aeqId5a03d806387f4b5d8b5de0172913af28(   )
A.eqId4d7ec2dffbe84f23a58544c843e9b95aB.eqId754f577d7d5045b995def9270dc83851C.eqId9dfcf17f255d44a993099870a9c7aabcD.eqId57b647f15ddb4f308c343ba86b32814b
6 . 函数eqId6f13759e937144069819aed2ae5a1057是定义域为R的奇函数,当eqIdaa1312dcc8e24925b421f7767761a363时,eqIdfa92db1cd77c4e0b8620170a903e1c2c,则当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqId6f13759e937144069819aed2ae5a1057的表达式为(   )
A.eqId7519a0c196564402925db981dea613e7B.eqId5e1ac45cd654415e8fac87f875b58e50C.eqId266f99093e0b41599996f6991156373fD.eqIdffdb3556999146d2b461c9c4ce2ccb73
填空题 | 较易(0.85) | 2021·浙江瑞安中学高一期中
7 . 已知定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数,当eqId4db620a5946b4ee0a9f530f35a6d505a时有eqId7c08a9e4c10f4d58b88d4a9fb7918a75,则eqId5a03d806387f4b5d8b5de0172913af28__________.
8 . 有下列几个命题,其中正确的命题是(   )
A.函数yeqId73569b6b04e14d5495df7ef0fbcbd02a在(-∞,-1)∪(-1,+∞)上是减函数;
B.函数yeqId4e64be836ca6495890b98b4f39982bcb的单调区间是[-2,+∞);
C.已知f(x)在R上是增函数,若ab>0,则有f(a)+f(b)>f(-a)+f(-b);
D.已知函数g(x)=eqIde086a8717f11431d9237e208bbec6256是奇函数,则f(x)=2x+3.
9 . 已知函数eqId10852d81bc184140a7780250c82c6929的图象关于原点对称,且当eqId4db620a5946b4ee0a9f530f35a6d505a时,eqIdffa218bea72e4cc48ba9e7ac0945d10a,则当eqIdaa1312dcc8e24925b421f7767761a363时,eqId2572ba99435645ad86330d89061cd3a3 ___________.
10 . 已知eqId6f13759e937144069819aed2ae5a1057定义域为eqId4758fc80638b4cac8e16b01028e6ab78的奇函数,当eqIdaa1312dcc8e24925b421f7767761a363时,eqIdeea6dcc8581f454dbc156ff2c62f0cae
求:(1)eqId6f13759e937144069819aed2ae5a1057的解析式.
(2)eqId6f13759e937144069819aed2ae5a1057零点.