新高考數(shù)學(xué)二輪復(fù)習(xí)創(chuàng)新題型專題02 函數(shù)與導(dǎo)數(shù)（新定義）（原卷版）

專題02函數(shù)與導(dǎo)數(shù)（新定義）一、單選題1．（2023·河南·洛陽市第三中學(xué)校聯(lián)考一模）高斯是德國(guó)著名的數(shù)學(xué)家，近代數(shù)學(xué)的奠基者之一，享有“數(shù)學(xué)王子”的稱號(hào)，用其名字命名的“高斯函數(shù)”為：設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過x的最大整數(shù)，則SKIPIF1<0稱為“高斯函數(shù)”，例如：SKIPIF1<0.已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2019秋·安徽蕪湖·高一蕪湖一中?？茧A段練習(xí)）在實(shí)數(shù)集SKIPIF1<0中定義一種運(yùn)算“SKIPIF1<0”，具有下列性質(zhì)：①對(duì)任意a，SKIPIF1<0，SKIPIF1<0；②對(duì)任意SKIPIF1<0，SKIPIF1<0；③對(duì)任意a，SKIPIF1<0，SKIPIF1<0．則函數(shù)SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·上?！そy(tǒng)考模擬預(yù)測(cè)）設(shè)SKIPIF1<0，若正實(shí)數(shù)SKIPIF1<0滿足：SKIPIF1<0則下列選項(xiàng)一定正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022秋·江蘇常州·高一華羅庚中學(xué)?？茧A段練習(xí)）對(duì)于函數(shù)SKIPIF1<0，若存在SKIPIF1<0，使SKIPIF1<0，則稱點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0是函數(shù)SKIPIF1<0的一對(duì)“隱對(duì)稱點(diǎn)”.若函數(shù)SKIPIF1<0的圖象存在“隱對(duì)稱點(diǎn)”，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023·高二單元測(cè)試）能夠把橢圓SKIPIF1<0的周長(zhǎng)和面積同時(shí)分為相等的兩部分的函數(shù)稱為橢圓的“可分函數(shù)”，下列函數(shù)中不是橢圓的“可分函數(shù)”的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023秋·江蘇無錫·高一統(tǒng)考期末）設(shè)SKIPIF1<0，計(jì)算機(jī)程序中用SKIPIF1<0表示不超過x的最大整數(shù)，則SKIPIF1<0稱為取整函數(shù)．例如；SKIPIF1<0．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2023·山東菏澤·統(tǒng)考一模）定義在實(shí)數(shù)集SKIPIF1<0上的函數(shù)SKIPIF1<0，如果SKIPIF1<0，使得SKIPIF1<0，則稱SKIPIF1<0為函數(shù)SKIPIF1<0的不動(dòng)點(diǎn).給定函數(shù)SKIPIF1<0，SKIPIF1<0，已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上均存在唯一不動(dòng)點(diǎn)，分別記為SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022秋·河北邢臺(tái)·高一統(tǒng)考期末）在定義域內(nèi)存在SKIPIF1<0，使得SKIPIF1<0成立的冪函數(shù)稱為“親冪函數(shù)”，則下列函數(shù)是“親冪函數(shù)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022秋·廣東深圳·高一深圳外國(guó)語學(xué)校校考期末）對(duì)實(shí)數(shù)a與b，定義新運(yùn)算SKIPIF1<0:SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象與x軸恰有兩個(gè)公共點(diǎn)，則實(shí)數(shù)c的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．（2022秋·山東日照·高一統(tǒng)考期末）已知符號(hào)函數(shù)SKIPIF1<0則“SKIPIF1<0”是“SKIPIF1<0”的（

）A．充要條件 B．充分不必要條件C．必要不充分條件 D．既不充分也不必要條件11．（2023秋·山東濰坊·高一統(tǒng)考期末）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，若SKIPIF1<0，滿足SKIPIF1<0，則稱函數(shù)SKIPIF1<0具有性質(zhì)SKIPIF1<0．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0具有性質(zhì)SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2023秋·青海西寧·高一統(tǒng)考期末）定義：對(duì)于SKIPIF1<0定義域內(nèi)的任意一個(gè)自變量的值SKIPIF1<0，都存在唯一一個(gè)SKIPIF1<0使得SKIPIF1<0成立，則稱函數(shù)SKIPIF1<0為“正積函數(shù)”.下列函數(shù)是“正積函數(shù)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2023·全國(guó)·高三專題練習(xí)）定義：在區(qū)間SKIPIF1<0上，若函數(shù)SKIPIF1<0是減函數(shù)，且SKIPIF1<0是增函數(shù)，則稱SKIPIF1<0在區(qū)間SKIPIF1<0上是“弱減函數(shù)”.若SKIPIF1<0在SKIPIF1<0上是“弱減函數(shù)”，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2022秋·山東青島·高三統(tǒng)考期末）已知定義域?yàn)镾KIPIF1<0的“類康托爾函數(shù)”SKIPIF1<0滿足：①SKIPIF1<0，SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0.則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．（2016·遼寧沈陽·東北育才學(xué)校?？家荒＃┒x兩種運(yùn)算：SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0的解析式為（

）A．SKIPIF1<0，SKIPIF1<0B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0D．SKIPIF1<0，SKIPIF1<016．（2023·全國(guó)·高三對(duì)口高考）定義SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．（2022秋·廣西河池·高一校聯(lián)考階段練習(xí)）定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，若對(duì)于任意的SKIPIF1<0，恒有SKIPIF1<0，則稱函數(shù)SKIPIF1<0為“純函數(shù)”，給出下列四個(gè)函數(shù)（1）SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0；（4）SKIPIF1<0，則下列函數(shù)中純函數(shù)個(gè)數(shù)是（

）A．0 B．1 C．2 D．318．（2021秋·上海黃浦·高三上海市大同中學(xué)?？计谥校?duì)于函數(shù)SKIPIF1<0，若集合SKIPIF1<0中恰有SKIPIF1<0個(gè)元素，則稱函數(shù)SKIPIF1<0是“SKIPIF1<0階準(zhǔn)奇函數(shù)”．若函數(shù)SKIPIF1<0，則SKIPIF1<0是“（

）階準(zhǔn)奇函數(shù)”．A．1 B．2 C．3 D．419．（2022秋·上海徐匯·高一位育中學(xué)?？茧A段練習(xí)）定義SKIPIF1<0為不小于SKIPIF1<0的最小整數(shù)（例如：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<020．（2022秋·浙江杭州·高一杭州四中?？计谥校┰O(shè)SKIPIF1<0是SKIPIF1<0上的任意實(shí)值函數(shù)．如下定義兩個(gè)函數(shù)SKIPIF1<0和SKIPIF1<0，對(duì)任意SKIPIF1<0，SKIPIF1<0，則下列等式不恒成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<021．（2021秋·上海徐匯·高一上海中學(xué)校考期末）已知SKIPIF1<0，SKIPIF1<0是定義在SKIPIF1<0上的嚴(yán)格增函數(shù)，SKIPIF1<0，若對(duì)任意SKIPIF1<0，存在SKIPIF1<0，使得SKIPIF1<0成立，則稱SKIPIF1<0是SKIPIF1<0在SKIPIF1<0上的“追逐函數(shù)”．已知SKIPIF1<0，則下列四個(gè)函數(shù)中是SKIPIF1<0在SKIPIF1<0上的“追逐函數(shù)”的個(gè)數(shù)為（

）個(gè)．①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0；④SKIPIF1<0．A．1 B．2 C．3 D．422．（2022秋·黑龍江哈爾濱·高一?？计谥校┤绻瘮?shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且值域?yàn)镾KIPIF1<0，則稱SKIPIF1<0為“SKIPIF1<0函數(shù)．已知函數(shù)SKIPIF1<0是“SKIPIF1<0函數(shù)，則m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．（2022秋·河南周口·高一?？计谥校?duì)于函數(shù)SKIPIF1<0，若對(duì)任意的SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為某一三角形的三邊長(zhǎng)，則稱SKIPIF1<0為“可構(gòu)成三角形的函數(shù)”，已知SKIPIF1<0是可構(gòu)成三角形的函數(shù)，則實(shí)數(shù)t的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2021秋·浙江嘉興·高一校聯(lián)考期中）定義SKIPIF1<0，如SKIPIF1<0．則函數(shù)SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2023·高一課時(shí)練習(xí)）函數(shù)SKIPIF1<0滿足在定義域內(nèi)存在非零實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0，則稱函數(shù)SKIPIF1<0為“有偶函數(shù)”．若函數(shù)SKIPIF1<0是在SKIPIF1<0上的“有偶函數(shù)”，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．（2020秋·北京順義·高一牛欄山一中?？计谥校┐嬖趦蓚€(gè)常數(shù)SKIPIF1<0和SKIPIF1<0，設(shè)函數(shù)的定義域?yàn)镾KIPIF1<0，則稱函數(shù)SKIPIF1<0在SKIPIF1<0上有界.下列函數(shù)中在其定義域上有界的個(gè)數(shù)為（

）①SKIPIF1<0②SKIPIF1<0；③SKIPIF1<0A．0 B．1 C．2 D．327．（2022秋·江蘇連云港·高一校考階段練習(xí)）對(duì)于函數(shù)SKIPIF1<0，如果存在區(qū)間SKIPIF1<0，同時(shí)滿足下列條件：①SKIPIF1<0在SKIPIF1<0內(nèi)是單調(diào)的；②當(dāng)定義域是SKIPIF1<0時(shí)，SKIPIF1<0的值域也是SKIPIF1<0，則稱SKIPIF1<0是該函數(shù)的“和諧區(qū)間”SKIPIF1<0若函數(shù)SKIPIF1<0存在“和諧區(qū)間”，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<028．（2022秋·安徽滁州·高三校考階段練習(xí)）對(duì)于定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0，若存在非零實(shí)數(shù)SKIPIF1<0，使函數(shù)SKIPIF1<0在SKIPIF1<0和SKIPIF1<0,SKIPIF1<0上與SKIPIF1<0軸均有交點(diǎn)，則稱SKIPIF1<0為函數(shù)SKIPIF1<0的一個(gè)“界點(diǎn)”．則下列四個(gè)函數(shù)中，不存在“界點(diǎn)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<029．（2022秋·江西景德鎮(zhèn)·高一江西省樂平中學(xué)?？茧A段練習(xí)）若函數(shù)SKIPIF1<0對(duì)任意SKIPIF1<0且SKIPIF1<0，都有SKIPIF1<0，則稱函數(shù)SKIPIF1<0為“穿透”函數(shù)，則下列函數(shù)中，不是“穿透”函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<030．（2023秋·陜西咸陽·高二武功縣普集高級(jí)中學(xué)統(tǒng)考期末）已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0，若存在SKIPIF1<0使得SKIPIF1<0，則稱SKIPIF1<0是SKIPIF1<0的一個(gè)“巧值點(diǎn)”，下列選項(xiàng)中沒有“巧值點(diǎn)”的函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<031．（2023·全國(guó)·高三專題練習(xí)）最近公布的2021年網(wǎng)絡(luò)新詞，我們非常熟悉的有“SKIPIF1<0”、“內(nèi)卷”、“躺平”等．定義方程SKIPIF1<0的實(shí)數(shù)根SKIPIF1<0叫做函數(shù)SKIPIF1<0的“躺平點(diǎn)”．若函數(shù)SKIPIF1<0，SKIPIF1<0的“躺平點(diǎn)”分別為SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<032．（2022·高二課時(shí)練習(xí)）設(shè)函數(shù)SKIPIF1<0在SKIPIF1<0上的導(dǎo)函數(shù)為SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上的導(dǎo)函數(shù)為SKIPIF1<0，若在SKIPIF1<0上SKIPIF1<0恒成立，則稱函數(shù)SKIPIF1<0在SKIPIF1<0上為“凸函數(shù)”.已知SKIPIF1<0在SKIPIF1<0上為“凸函數(shù)”，則實(shí)數(shù)t的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<033．（2022秋·廣東深圳·高三校考階段練習(xí)）定義方程SKIPIF1<0的實(shí)根SKIPIF1<0叫做函數(shù)SKIPIF1<0的“新駐點(diǎn)”，若函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的“新駐點(diǎn)”分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<034．（2022春·山東·高三山東師范大學(xué)附中校考期中）定義滿足方程SKIPIF1<0的解SKIPIF1<0叫做函數(shù)SKIPIF1<0的“自足點(diǎn)”，則下列函數(shù)不存在“自足點(diǎn)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題35．（2023秋·陜西渭南·高一統(tǒng)考期末）對(duì)于定義域?yàn)镾KIPIF1<0的函數(shù)SKIPIF1<0，若存在區(qū)間SKIPIF1<0，使得SKIPIF1<0同時(shí)滿足，①SKIPIF1<0在SKIPIF1<0上是單調(diào)函數(shù)，②當(dāng)SKIPIF1<0的定義域?yàn)镾KIPIF1<0時(shí)，SKIPIF1<0的值域也為SKIPIF1<0，則稱區(qū)間SKIPIF1<0為該函數(shù)的一個(gè)“和諧區(qū)間”，則（

）A．函數(shù)SKIPIF1<0有3個(gè)“和諧區(qū)間”；B．函數(shù)SKIPIF1<0，SKIPIF1<0存在“和諧區(qū)間”C．若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0有“和諧區(qū)間”，實(shí)數(shù)SKIPIF1<0的取值范圍為SKIPIF1<0D．若函數(shù)SKIPIF1<0有“和諧區(qū)間”，則實(shí)數(shù)SKIPIF1<0的取值范圍為SKIPIF1<036．（2023秋·云南昆明·高一昆明一中統(tǒng)考期末）已知?dú)W拉函數(shù)SKIPIF1<0的函數(shù)值等于所有不超過正整數(shù)SKIPIF1<0，且與SKIPIF1<0互素的正整數(shù)的個(gè)數(shù)，例如：SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0是單調(diào)遞增函數(shù) B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值為SKIPIF1<0C．當(dāng)SKIPIF1<0為素?cái)?shù)時(shí)，SKIPIF1<0 D．當(dāng)SKIPIF1<0為偶數(shù)時(shí)，SKIPIF1<037．（2022秋·河北邢臺(tái)·高一統(tǒng)考期末）對(duì)于函數(shù)SKIPIF1<0，若在區(qū)間SKIPIF1<0上存在SKIPIF1<0，使得SKIPIF1<0，則稱SKIPIF1<0是區(qū)間SKIPIF1<0上的“穩(wěn)定函數(shù)”.下列函數(shù)中，是區(qū)間SKIPIF1<0上的“穩(wěn)定函數(shù)”的有（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<038．（2023秋·湖北襄陽·高一統(tǒng)考期末）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0的圖象連續(xù)不斷，若存在常數(shù)SKIPIF1<0，使得SKIPIF1<0對(duì)于任意的實(shí)數(shù)SKIPIF1<0恒成立，則稱SKIPIF1<0是回旋函數(shù).給出下列四個(gè)命題，正確的命題是（

）A．函數(shù)SKIPIF1<0（其中SKIPIF1<0為常數(shù)，SKIPIF1<0為回旋函數(shù)的充要條件是SKIPIF1<0B．函數(shù)SKIPIF1<0是回旋函數(shù)C．若函數(shù)SKIPIF1<0為回旋函數(shù)，則SKIPIF1<0D．函數(shù)SKIPIF1<0是SKIPIF1<0的回旋函數(shù)，則SKIPIF1<0在SKIPIF1<0上至少有1011個(gè)零點(diǎn)39．（2023秋·河南周口·高一統(tǒng)考期末）若函數(shù)SKIPIF1<0同時(shí)滿足：①對(duì)于定義域上的任意x，恒有SKIPIF1<0；②若對(duì)于定義域上的任意SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0，則稱函數(shù)SKIPIF1<0為“理想函數(shù)”.下列四個(gè)函數(shù)中，能被稱為“理想函數(shù)”的有（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<040．（2023秋·遼寧沈陽·高一沈陽市第十中學(xué)?？计谀┑聡?guó)數(shù)學(xué)家高斯在證明“二次互反律”的過程中，首次定義了取整函數(shù)SKIPIF1<0，表示“不超過SKIPIF1<0的最大整數(shù)”，后來我們又把函數(shù)SKIPIF1<0稱為“高斯函數(shù)”，關(guān)于SKIPIF1<0下列說法正確的是（

）A．對(duì)任意SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0B．函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0或SKIPIF1<0C．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D．SKIPIF1<041．（2023·山東臨沂·高一校考期末）華人數(shù)學(xué)家李天巖和美國(guó)數(shù)學(xué)家約克給出了“混沌”的數(shù)學(xué)定義，由此發(fā)展的混沌理論在生物學(xué)?經(jīng)濟(jì)學(xué)和社會(huì)學(xué)領(lǐng)域都有重要作用.在混沌理論中，函數(shù)的周期點(diǎn)是一個(gè)關(guān)鍵概念，定義如下：設(shè)SKIPIF1<0是定義在R上的函數(shù)，對(duì)于SKIPIF1<0，令SKIPIF1<0，若存在正整數(shù)k使得SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則稱SKIPIF1<0值是SKIPIF1<0的一個(gè)周期為k的周期點(diǎn)．若SKIPIF1<0，下列各值是SKIPIF1<0周期為2的周期點(diǎn)的有（

）A．0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<042．（2022秋·河南漯河·高一漯河四高校考期末）設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，若對(duì)于任意SKIPIF1<0，存在SKIPIF1<0使SKIPIF1<0（SKIPIF1<0為常數(shù)）成立，則稱函數(shù)SKIPIF1<0在SKIPIF1<0上的“半差值”為SKIPIF1<0下列四個(gè)函數(shù)中，滿足所在定義域上“半差值”為SKIPIF1<0的函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<043．（2023秋·上海崇明·高一統(tǒng)考期末）已知函數(shù)SKIPIF1<0的定義域?yàn)镈，對(duì)于D中任意給定的實(shí)數(shù)x，都有SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0SKIPIF1<0．則下列3個(gè)命題中是真命題的有_____________（填寫所有的真命題序號(hào)）．①若SKIPIF1<0，則SKIPIF1<0；②若當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值5，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最小值SKIPIF1<0；③若SKIPIF1<0在區(qū)間SKIPIF1<0上是嚴(yán)格增函數(shù)，則SKIPIF1<0在區(qū)間SKIPIF1<0上是嚴(yán)格減函數(shù)．44．（2022秋·上海寶山·高二上海市吳淞中學(xué)?？奸_學(xué)考試）函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，滿足：①SKIPIF1<0在SKIPIF1<0內(nèi)是單調(diào)函數(shù)；②存在SKIPIF1<0，使得SKIPIF1<0在SKIPIF1<0上的值域?yàn)镾KIPIF1<0，那么就稱函數(shù)SKIPIF1<0為“優(yōu)美函數(shù)”，若函數(shù)SKIPIF1<0是“優(yōu)美函數(shù)”，則SKIPIF1<0的取值范圍是___________.45．（2023秋·山東德州·高一統(tǒng)考期末）在數(shù)學(xué)中連乘符號(hào)是“SKIPIF1<0”，這個(gè)符號(hào)就是連續(xù)求積的意思，把滿足“SKIPIF1<0”這個(gè)符號(hào)下面條件的所有項(xiàng)都乘起來，例如：SKIPIF1<0．函數(shù)SKIPIF1<0，定義使SKIPIF1<0為整數(shù)的數(shù)SKIPIF1<0叫做企盼數(shù)，則在區(qū)間SKIPIF1<0內(nèi)，這樣的企盼數(shù)共有_______個(gè)．46．（2021春·福建三明·高二三明一中?？茧A段練習(xí)）對(duì)于函數(shù)SKIPIF1<0可以采用下列方法求導(dǎo)數(shù)：由SKIPIF1<0可得SKIPIF1<0，兩邊求導(dǎo)可得SKIPIF1<0，故SKIPIF1<0.根據(jù)這一方法，可得函數(shù)SKIPIF1<0的極小值為___________.47．（2021春·重慶渝北·高二重慶市兩江中學(xué)校?？茧A段練習(xí)）設(shè)SKIPIF1<0與SKIPIF1<0是定義在同一區(qū)間SKIPIF1<0上的兩個(gè)函數(shù)，若函數(shù)SKIPIF1<0在SKIPIF1<0上有兩個(gè)不同的零點(diǎn)，則稱SKIPIF1<0與SKIPIF1<0在SKIPIF1<0上是“關(guān)聯(lián)函數(shù)”．若SKIPIF1<0與SKIPIF1<0在SKIPIF1<0上是“關(guān)聯(lián)函數(shù)”，則實(shí)數(shù)SKIPIF1<0的取值范圍是____________．48．（2018春·河南南陽·高二統(tǒng)考期中）定義：如果函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在SKIPIF1<0，SKIPIF1<0（SKIPIF1<0），滿足SKIPIF1<0，SKIPIF1<0，則稱函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是一個(gè)雙中值函數(shù)，已知函數(shù)SKIPIF1<0是區(qū)間SKIPIF1<0上的雙中值函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是__________．四、解答題49．（2023·全國(guó)·高三專題練習(xí)）在數(shù)學(xué)中，布勞威爾不動(dòng)點(diǎn)定理是拓?fù)鋵W(xué)里一個(gè)非常重要的不動(dòng)點(diǎn)定理，它可運(yùn)用到有限維空間并構(gòu)成了一般不動(dòng)點(diǎn)定理的基石.布勞威爾不動(dòng)點(diǎn)定理得名于荷蘭數(shù)學(xué)家魯伊茲·布勞威爾（L.E.J.Brouwer）.簡(jiǎn)單地講就是：對(duì)于滿足一定條件的連續(xù)函數(shù)SKIPIF1<0，存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0，我們就稱該函數(shù)“不動(dòng)點(diǎn)”函數(shù)，實(shí)數(shù)SKIPIF1<0為該函數(shù)的不動(dòng)點(diǎn).(1)求函數(shù)SKIPIF1<0的不動(dòng)點(diǎn)；(2)若函數(shù)SKIPIF1<0有兩個(gè)不動(dòng)點(diǎn)SKIPIF1<0，且SKIPIF1<0