组卷网>知识点选题>利用函数奇偶性解抽象函数不等式
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2 . 已知定义在eqId38a1a72a865d4179b3b243977e23dce4上的奇函数eqId4837c94ef0ff4dcf9b1dda4df363275aeqId176a569ddabd4e4482d9ab5af6e2d6ea上单调递增,且eqId7627c6e38ce14a8f891bce4571b5830e,若实数x满足eqIdb4befa6b560948d190f7214b0a2b0e59,则x的取值范围是(   )
A.eqId71fc87592d564951b3584d59ae5501f3B.eqIdff2cd0f3f4ad4bb79aceaacc8c2ced04C.eqIdce5c14600d8f4658abc96f8e6d822b81D.eqId7b066873a64c45fc84083dade18a1334
3 . 设函数eqIdbbc4df94a65b4983bd36e80b8cbaa4ab是奇函数eqId994d0c2c71774874a3db7e06ebdd54df的导函数,eqId09747310449f44db82d14dc68ef62c79.当eqId2d569479cd1c43c1af15895792b64db6时,eqId44f12629c774417692870900d892e94c,则使得eqIdbe432bb56dcd448c88dddd29491deec5成立的eqIda9cd3f94eb8045438f75e9daccfa7200的取值范围是(   )
A.eqId277d0292215944c985f637a9aa1e3298B.eqIdbec24efcde7442a982916a4de3f3b84a
C.eqIdb8a4341b3b174c73b52cab9f4dc460d6D.eqId7efc55bb8460435581a8f334e3a576c5
5 . 已知函数eqId6f13759e937144069819aed2ae5a1057是定义在R上的奇函数,其导函数为eqId39f6d0ac61bb453890de392f136c3074,当eqId2d569479cd1c43c1af15895792b64db6时,eqIdf12354340a044b4a930fdd7d330d8030,若eqIda1e26e78ecec4c6fa2a2a6ef42063bf3则不等式eqId789ec6dfca674cdda55d613db82bd57c的解集为____________.
6 . 已知函数eqIdfa5e38f3901448a194292db770c1c314为奇函数.
(1)求实数eqIda4be99d332154d13a4a6ed1ff6444fe7的值;
(2)判断并证明函数eqId4837c94ef0ff4dcf9b1dda4df363275a的单调性;
(3)求不等式eqIdb60e6465ecc746f3bf1979ea9fe4c1a0的解集.
8 . 已知定义域为R的函数eqId0f9a63373e8b414b8a04853565aefbd1是奇函数.
(1)求ab的值;
(2)若对在意的eqIdf8e289a6ed19487eba157e5ea460a84e,不等式eqId62c7d39bfd6749c08c596ecda6ad9083恒成立,求k的取值范围.
9 . 已知定义域为eqId38a1a72a865d4179b3b243977e23dce4的单调减函数eqId4837c94ef0ff4dcf9b1dda4df363275a是奇函数,当eqId2d569479cd1c43c1af15895792b64db6时,eqId9664b0a5c84b41558a5cd89dbc99a1e5.
(1)求eqId1178211e197e42ac83119f21246240ad的值;
(2)求eqId4837c94ef0ff4dcf9b1dda4df363275a的解析式;
(3)若任意eqId5d512c2d1a1b4a6b9d2f825cff522875,不等式eqId6781a7fef6cc437c846add13d03d76ab恒成立,求实数eqId4d2187284c5d4de29906363f7d21f60f的取值范围.
10 . 若不恒为零的函数eqId144eff5c0e4649138a21f2b1b6a06907对任意eqId7431d070400e4b3c9f15d6551249c176,恒有eqIde38efa5a20a34633aee047869ed47f99
(1)指出eqId144eff5c0e4649138a21f2b1b6a06907的奇偶性,并给予证明;
(2)若eqId2d569479cd1c43c1af15895792b64db6时,eqId0836c1003605494a89734a73b75e144c,证明eqId6f13759e937144069819aed2ae5a1057eqId7dcd2312d0bf4bb1befdfcc170e45791上单调递减;
(3)在(2)的条件下,若对任意实数x,恒有eqId4b68db3904e348c4989a7dd926d3c69c成立,求实数k的取值范围.
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