From d796a5f67ef574412180a5afa3f0026e6d660e6d Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Tue, 12 Mar 2024 19:00:38 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0K02\d{5}B=E7=9A=84=E7=9B=AE?= =?UTF-8?q?=E6=A0=87=E7=9A=84predecessor?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/LessonObj.json | 425 ++++++++++++++++++++++++++++++++--------- 1 file changed, 335 insertions(+), 90 deletions(-) diff --git a/题库0.3/LessonObj.json b/题库0.3/LessonObj.json index 30e902fa..c64a4602 100644 --- a/题库0.3/LessonObj.json +++ b/题库0.3/LessonObj.json @@ -494,67 +494,96 @@ "id": "K0201002B", "unit_obj": "D02001B", "content": "理解根式及其相关的概念.", - "predecessor": [] + "predecessor": [ + "K0201001B" + ] }, "K0201003B": { "id": "K0201003B", "unit_obj": "D02001B", "content": "会根据定义求实数的$n$次方根.", - "predecessor": [] + "predecessor": [ + "K0201002B" + ] }, "K0201004B": { "id": "K0201004B", "unit_obj": "D02001B", "content": "理解底数为正实数$a$的有理数指数幂的定义$a^{m/n}=(a^{m})^{1/n}$,经历等价定义$a^{m/n}= (a^{1/n})^{m}$的推导过程.", - "predecessor": [] + "predecessor": [ + "K0201001B", + "K0201002B" + ] }, "K0202001B": { "id": "K0202001B", "unit_obj": "D02001B", "content": "经历在个别情形下验证底数为正实数的有理数指数幂的三条运算性质的过程.", - "predecessor": [] + "predecessor": [ + "K0201001B", + "K0201004B" + ] }, "K0202002B": { "id": "K0202002B", "unit_obj": "D02001B", "content": "会运用底数为正实数的有理数指数幂的定义及运算性质进行幂与根式的互化以及解决相关的化简、计算等问题.", - "predecessor": [] + "predecessor": [ + "K0201004B", + "K0202001B" + ] }, "K0202003B": { "id": "K0202003B", "unit_obj": "D02001B", "content": "理解底数为负实数的有理数指数幂的定义, 进而理解底数为实数的有理数指数幂的定义.", - "predecessor": [] + "predecessor": [ + "K0202002B" + ] }, "K0203001B": { "id": "K0203001B", "unit_obj": "D02001B", "content": "知道底数为正实数的无理数指数幂的定义.", - "predecessor": [] + "predecessor": [ + "K0202002B" + ] }, "K0203002B": { "id": "K0203002B", "unit_obj": "D02001B", "content": "熟记底数为正实数的实数指数幂的三条运算性质.", - "predecessor": [] + "predecessor": [ + "K0202002B", + "K0202001B" + ] }, "K0203003B": { "id": "K0203003B", "unit_obj": "D02001B", "content": "经历有理数指数幂的基本不等式: ``当实数$a>1$, 有理数$s>0$时, 不等式$a^s>1$成立''的推导过程.", - "predecessor": [] + "predecessor": [ + "K0202003B" + ] }, "K0203004B": { "id": "K0203004B", "unit_obj": "D02001B", "content": "知道幂的基本不等式: ``当$a>1$, $s>0$时, $a^s>1$''.", - "predecessor": [] + "predecessor": [ + "K0203002B" + ] }, "K0203005B": { "id": "K0203005B", "unit_obj": "D02001B", "content": "会应用底数为正实数的实数指数幂的定义、运算性质以及幂的基本不等式, 解决底数为正实数的实数指数幂的较复杂的表达式的化简、不等式的证明等问题.", - "predecessor": [] + "predecessor": [ + "K0202002B", + "K0203001B", + "K0203002B", + "K0203004B" + ] }, "K0204001B": { "id": "K0204001B", @@ -566,49 +595,73 @@ "id": "K0204002B", "unit_obj": "D02001B", "content": "会理解、熟记并应用一些常用的对数等式: ``$a^{\\log_aN}=N$, $\\log_a1=0$, $\\log_aa=1$''.", - "predecessor": [] + "predecessor": [ + "K0204001B" + ] }, "K0204003B": { "id": "K0204003B", "unit_obj": "D02001B", "content": "知道常用对数、常数$e$以及自然对数的含义.", - "predecessor": [] + "predecessor": [ + "K0204001B" + ] }, "K0204004B": { "id": "K0204004B", "unit_obj": "D02001B", "content": "会进行指数式与对数式的互化, 以及对数式的化简.", - "predecessor": [] + "predecessor": [ + "K0204001B", + "K0204003B" + ] }, "K0205001B": { "id": "K0205001B", "unit_obj": "D02001B", "content": "经历推导对数运算性质$1$: ``当$M>0$,$N>0$时, $\\log_a(MN)=\\log_aM+\\log_aN$''；性质$2$: ``当$M>0$,$N>0$时, $\\log_a(M/N)=\\log_aM-\\log_aN$''；性质$3$: ``当$N>0$时, 对任何给定的实数$c$, $\\log_a(N^{c})=c\\log_aN$''的过程, 并熟记这三条运算性质.", - "predecessor": [] + "predecessor": [ + "K0204001B", + "K0203002B" + ] }, "K0205002B": { "id": "K0205002B", "unit_obj": "D02001B", "content": "会运用对数的定义以及运算性质解决简单的求值、化简以及生活实际问题.", - "predecessor": [] + "predecessor": [ + "K0204001B", + "K0205001B" + ] }, "K0206001B": { "id": "K0206001B", "unit_obj": "D02001B", "content": "经历推导对数换底公式的过程.", - "predecessor": [] + "predecessor": [ + "K0205001B", + "K0204003B", + "K0204002B" + ] }, "K0206002B": { "id": "K0206002B", "unit_obj": "D02001B", "content": "会运用对数的运算性质以及换底公式解决较复杂的求值、化简以及证明等相关问题.", - "predecessor": [] + "predecessor": [ + "K0205001B", + "K0206001B" + ] }, "K0206003B": { "id": "K0206003B", "unit_obj": "D02001B", "content": "会推导并会运用例7的结论: ``当$a>0$, $a\\neq1$, 且$N>0$, $m\\neq0$时, $\\log_a^{m}N^{n}=n/m\\log_aN$''.", - "predecessor": [] + "predecessor": [ + "K0206001B", + "K0205001B", + "K0204002B" + ] }, "K0207001B": { "id": "K0207001B", @@ -620,31 +673,43 @@ "id": "K0207002B", "unit_obj": "D02002B", "content": "会根据具体的幂指数$a$求解幂函数$y=x^{a}$的定义域.", - "predecessor": [] + "predecessor": [ + "K0207001B", + "K0202003B" + ] }, "K0207003B": { "id": "K0207003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出幂函数$y=x^{1/2}$, $y=x^{3}$, $y=x^{-2/3}$的大致图像.", - "predecessor": [] + "predecessor": [ + "K0207002B" + ] }, "K0207004B": { "id": "K0207004B", "unit_obj": "D02002B", "content": "会用图像上任意一点关于原点(或关于$y$轴)的对称点仍落在图像上证明函数的图像关于原点(或$y$轴)对称.", - "predecessor": [] + "predecessor": [ + "K0207003B" + ] }, "K0208001B": { "id": "K0208001B", "unit_obj": "D02002B", "content": "会用不等式的常用性质证明当$x>0$时, 幂函数的函数值总大于$0$.", - "predecessor": [] + "predecessor": [ + "K0111001B" + ] }, "K0208002B": { "id": "K0208002B", "unit_obj": "D02002B", "content": "会经历作图猜想证明具体的幂函数图像在第一象限的单调性.", - "predecessor": [] + "predecessor": [ + "K0203004B", + "K0207003B" + ] }, "K0208003B": { "id": "K0208003B", @@ -656,7 +721,9 @@ "id": "K0208004B", "unit_obj": "D02002B", "content": "会用幂函数的单调性判断两个幂的大小.", - "predecessor": [] + "predecessor": [ + "K0208002B" + ] }, "K0208005B": { "id": "K0208005B", @@ -668,289 +735,414 @@ "id": "K0209001B", "unit_obj": "D02002B", "content": "理解指数函数的定义(包含指数函数定义域为$\\mathbf{R}$).", - "predecessor": [] + "predecessor": [ + "K0202003B", + "K0203001B" + ] }, "K0209002B": { "id": "K0209002B", "unit_obj": "D02002B", "content": "会求解有关指数型函数的定义域.", - "predecessor": [] + "predecessor": [ + "K0202002B", + "K0203001B" + ] }, "K0209003B": { "id": "K0209003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出指数函数$y=2^{x}$, $y=3^{x}$, $y=(1/2)^{x}$的大致图像.", - "predecessor": [] + "predecessor": [ + "K0209001B" + ] }, "K0210001B": { "id": "K0210001B", "unit_obj": "D02002B", "content": "会结合图像, 了解指数函数函数值恒大于$0$.", - "predecessor": [] + "predecessor": [ + "K0209003B" + ] }, "K0210002B": { "id": "K0210002B", "unit_obj": "D02002B", "content": "知道指数函数图像过定点$(0,1)$.", - "predecessor": [] + "predecessor": [ + "K0209003B" + ] }, "K0210003B": { "id": "K0210003B", "unit_obj": "D02002B", "content": "会证明指数函数$y=a^{x}$与$y=(1/a)^{x}$($a>0$且$a\\neq1$)的图像关于$y$轴对称.", - "predecessor": [] + "predecessor": [ + "K0203002B", + "K0209003B" + ] }, "K0210004B": { "id": "K0210004B", "unit_obj": "D02002B", "content": "会利用幂的基本不等式证明指数函数的单调性.", - "predecessor": [] + "predecessor": [ + "K0203004B" + ] }, "K0210005B": { "id": "K0210005B", "unit_obj": "D02002B", "content": "会作出指数函数的大致图像, 能根据其图像特征叙述其函数性质.", - "predecessor": [] + "predecessor": [ + "K0209003B", + "K0210001B", + "K0210002B", + "K0210004B" + ] }, "K0210006B": { "id": "K0210006B", "unit_obj": "D02002B", "content": "会利用指数函数的单调性判断两个数的大小.", - "predecessor": [] + "predecessor": [ + "K0210005B" + ] }, "K0211001B": { "id": "K0211001B", "unit_obj": "D02002B", "content": "会利用指数函数的单调性解决相关不等式等问题.", - "predecessor": [] + "predecessor": [ + "K0210005B" + ] }, "K0211002B": { "id": "K0211002B", "unit_obj": "D02002B", "content": "会利用指数函数的性质解决其他如最值问题等数学问题和实际生活问题.", - "predecessor": [] + "predecessor": [ + "K0210005B" + ] }, "K0212001B": { "id": "K0212001B", "unit_obj": "D02002B", "content": "理解对数函数的定义(包含对数函数定义域为$(0,+\\infty)$).", - "predecessor": [] + "predecessor": [ + "K0204001B" + ] }, "K0212002B": { "id": "K0212002B", "unit_obj": "D02002B", "content": "会求解有关对数型函数的定义域.", - "predecessor": [] + "predecessor": [ + "K0212001B" + ] }, "K0212003B": { "id": "K0212003B", "unit_obj": "D02002B", "content": "会根据函数定义域, 利用计算器合理采点, 并能通过描点法作出对数函数$y=\\log_2x,y=\\log_3x,y=\\log_{1/2}x$的大致图像.", - "predecessor": [] + "predecessor": [ + "K0212001B" + ] }, "K0213001B": { "id": "K0213001B", "unit_obj": "D02002B", "content": "会利用对数运算性质, 证明函数$y=\\log_ax,y=\\log_{1/a}x$的图像关于$x$轴对称.", - "predecessor": [] + "predecessor": [ + "K0212003B", + "K0206001B" + ] }, "K0213002B": { "id": "K0213002B", "unit_obj": "D02002B", "content": "知道对数函数的图像过定点$(1,0)$.", - "predecessor": [] + "predecessor": [ + "K0204002B" + ] }, "K0213003B": { "id": "K0213003B", "unit_obj": "D02002B", "content": "会联系幂的基本不等式, 利用反证法证明对数的基本不等式.", - "predecessor": [] + "predecessor": [ + "K0203004B", + "K0204001B", + "K0107003B" + ] }, "K0213004B": { "id": "K0213004B", "unit_obj": "D02002B", "content": "会类比指数函数的单调性的证明, 利用对数的基本不等式证明对数函数的单调性.", - "predecessor": [] + "predecessor": [ + "K0210004B", + "K0213003B" + ] }, "K0213005B": { "id": "K0213005B", "unit_obj": "D02002B", "content": "会结合图像以及指数与对数互为逆运算的性质, 探究并证明对数函数$y=\\log_ax$和指数函数$y=a^{x}$的图像关于直线$y=x$对称.", - "predecessor": [] + "predecessor": [ + "K0204001B", + "K0210005B", + "K0212003B" + ] }, "K0213006B": { "id": "K0213006B", "unit_obj": "D02002B", "content": "了解逆运算和反函数的概念.", - "predecessor": [] + "predecessor": [ + "K0213005B" + ] }, "K0213007B": { "id": "K0213007B", "unit_obj": "D02002B", "content": "会作出对数函数的大致图像, 能根据其图像特征叙述函数性质.", - "predecessor": [] + "predecessor": [ + "K0212003B", + "K0213001B", + "K0213002B", + "K0213004B" + ] }, "K0213008B": { "id": "K0213008B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性判断两个数的大小.", - "predecessor": [] + "predecessor": [ + "K0213007B" + ] }, "K0214001B": { "id": "K0214001B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性估算对数型无理数(如$\\log_23$).", - "predecessor": [] + "predecessor": [ + "K0213007B" + ] }, "K0214002B": { "id": "K0214002B", "unit_obj": "D02002B", "content": "会利用对数函数的单调性解决其他相关不等式等数学问题和生活中的实际问题.", - "predecessor": [] + "predecessor": [ + "K0213007B" + ] }, "K0215001B": { "id": "K0215001B", "unit_obj": "D02003B", "content": "理解函数的概念, 体会函数即数与数之间的对应关系, 理解函数的定义(包含自变量、函数值、定义域、值域的概念).", - "predecessor": [] + "predecessor": [ + "K0101001B" + ] }, "K0215002B": { "id": "K0215002B", "unit_obj": "D02003B", "content": "知道定义域和对应关系为函数的两个要素.", - "predecessor": [] + "predecessor": [ + "K0215001B" + ] }, "K0215003B": { "id": "K0215003B", "unit_obj": "D02003B", "content": "会求函数的自然定义域.", - "predecessor": [] + "predecessor": [ + "K0215001B", + "K0207002B", + "K0209002B", + "K0212002B", + "K0104001B" + ] }, "K0215004B": { "id": "K0215004B", "unit_obj": "D02003B", "content": "理解两个函数相同的定义, 并会判断两个函数是否是同一函数.", - "predecessor": [] + "predecessor": [ + "K0215002B" + ] }, "K0215005B": { "id": "K0215005B", "unit_obj": "D02003B", "content": "会根据已学习过的一些简单函数的值域, 利用复合求解稍为复杂函数的值域.", - "predecessor": [] + "predecessor": [ + "K0213007B", + "K0210005B" + ] }, "K0216001B": { "id": "K0216001B", "unit_obj": "D02003B", "content": "知道函数可以用解析式、图像、列表等方式表示.", - "predecessor": [] + "predecessor": [ + "K0215001B" + ] }, "K0216002B": { "id": "K0216002B", "unit_obj": "D02003B", "content": "理解函数的图像的概念.", - "predecessor": [] + "predecessor": [ + "K0215001B" + ] }, "K0216003B": { "id": "K0216003B", "unit_obj": "D02003B", "content": "会合理利用计算器采点, 通过描点法作出不熟悉函数的大致图像.", - "predecessor": [] + "predecessor": [ + "K0216002B" + ] }, "K0216004B": { "id": "K0216004B", "unit_obj": "D02003B", "content": "会利用函数的定义判断坐标系中的图像是否为函数图像.", - "predecessor": [] + "predecessor": [ + "K0215001B" + ] }, "K0216005B": { "id": "K0216005B", "unit_obj": "D02003B", "content": "了解并能根据实际情况运用函数的分段表示法.", - "predecessor": [] + "predecessor": [ + "K0216001B", + "K0215002B" + ] }, "K0216006B": { "id": "K0216006B", "unit_obj": "D02003B", "content": "知道取整符号$[x]$的含义, 并作出取整函数的大致图像.", - "predecessor": [] + "predecessor": [ + "K0216003B", + "K0216005B" + ] }, "K0217001B": { "id": "K0217001B", "unit_obj": "D02003B", "content": "知道基于点集的平面图形关于直线成轴对称, 以及关于点成中心对称的定义.", - "predecessor": [] + "predecessor": [ + "K0207003B" + ] }, "K0217002B": { "id": "K0217002B", "unit_obj": "D02003B", "content": "会推导``函数的图像关于$y$轴成轴对称''的等价的代数表达形式, 即偶函数的定义.", - "predecessor": [] + "predecessor": [ + "K0217001B" + ] }, "K0217003B": { "id": "K0217003B", "unit_obj": "D02003B", "content": "会类比偶函数的定义得到``函数的图像关于原点成中心对称''的等价的代数表达形式, 即奇函数的定义.", - "predecessor": [] + "predecessor": [ + "K0217002B" + ] }, "K0217004B": { "id": "K0217004B", "unit_obj": "D02003B", "content": "会运用奇函数、偶函数的定义, 证明一些较为简单的函数是奇函数或是偶函数.", - "predecessor": [] + "predecessor": [ + "K0217002B", + "K0217003B" + ] }, "K0218001B": { "id": "K0218001B", "unit_obj": "D02003B", "content": "会运用奇函数、偶函数的定义, 通过赋值法或分析定义域, 判断较为复杂(如含参数)的函数的奇偶性问题.", - "predecessor": [] + "predecessor": [ + "K0217004B" + ] }, "K0219001B": { "id": "K0219001B", "unit_obj": "D02003B", "content": "理解函数单调性的定义.", - "predecessor": [] + "predecessor": [ + "K0210004B", + "K0213004B" + ] }, "K0219002B": { "id": "K0219002B", "unit_obj": "D02003B", "content": "会运用函数单调性的定义证明一次函数、二次函数、反比例函数的单调性.", - "predecessor": [] + "predecessor": [ + "K0219001B" + ] }, "K0219003B": { "id": "K0219003B", "unit_obj": "D02003B", "content": "会运用函数单调性的定义以及已知的基本初等函数的单调性, 判断较为复杂的函数单调性.", - "predecessor": [] + "predecessor": [ + "K0210004B", + "K0213004B", + "K0219001B" + ] }, "K0220001B": { "id": "K0220001B", "unit_obj": "D02003B", "content": "理解单调函数、单调区间的定义.", - "predecessor": [] + "predecessor": [ + "K0219001B" + ] }, "K0220002B": { "id": "K0220002B", "unit_obj": "D02003B", "content": "会求函数的单调区间.", - "predecessor": [] + "predecessor": [ + "K0220001B" + ] }, "K0220003B": { "id": "K0220003B", "unit_obj": "D02003B", "content": "能直观地感知奇偶性可用于分析单调性并能说理.", - "predecessor": [] + "predecessor": [ + "K0220001B", + "K0217002B", + "K0217003B" + ] }, "K0221001B": { "id": "K0221001B", "unit_obj": "D02003B", "content": "理解函数最大值、最小值的定义.", - "predecessor": [] + "predecessor": [ + "K0215001B" + ] }, "K0221002B": { "id": "K0221002B", "unit_obj": "D02003B", "content": "会运用最值的定义, 解决函数的最值问题, 以及含参数的函数最值问题(函数对应关系含参数或者定义域含参数)的数学问题.", - "predecessor": [] + "predecessor": [ + "K0220002B", + "K0221001B" + ] }, "K0222001B": { "id": "K0222001B", @@ -962,79 +1154,119 @@ "id": "K0222002B", "unit_obj": "D02004B", "content": "在建立好的数学模型中, 能合理选取变量, 建立变量之间的函数关系, 并能结合实际写出函数的定义域.", - "predecessor": [] + "predecessor": [ + "K0222001B", + "K0215001B" + ] }, "K0223001B": { "id": "K0223001B", "unit_obj": "D02004B", "content": "知道函数零点的定义.", - "predecessor": [] + "predecessor": [ + "K0215001B", + "K0108002B" + ] }, "K0223002B": { "id": "K0223002B", "unit_obj": "D02004B", "content": "会用函数的观点求解一元二次方程.", - "predecessor": [] + "predecessor": [ + "K0223001B", + "K0109001B" + ] }, "K0223003B": { "id": "K0223003B", "unit_obj": "D02004B", "content": "会用函数的观点求解一元二次不等式.", - "predecessor": [] + "predecessor": [ + "K0223001B", + "K0112002B" + ] }, "K0223004B": { "id": "K0223004B", "unit_obj": "D02004B", "content": "会用函数的观点求解较为复杂的方程.", - "predecessor": [] + "predecessor": [ + "K0223001B", + "K0219003B" + ] }, "K0223005B": { "id": "K0223005B", "unit_obj": "D02004B", "content": "会用函数的观点求解较为复杂的不等式.", - "predecessor": [] + "predecessor": [ + "K0223001B", + "K0219003B" + ] }, "K0224001B": { "id": "K0224001B", "unit_obj": "D02004B", "content": "知道零点存在定理, 会用零点存在定理判断连续函数在区间上存在零点.", - "predecessor": [] + "predecessor": [ + "K0223001B", + "K0216003B" + ] }, "K0224002B": { "id": "K0224002B", "unit_obj": "D02004B", "content": "理解并会运用二分法寻求连续函数在某个区间上的零点的近似值.", - "predecessor": [] + "predecessor": [ + "K0224001B" + ] }, "K0225001B": { "id": "K0225001B", "unit_obj": "D02004B", "content": "理解反函数的定义.", - "predecessor": [] + "predecessor": [ + "K0213006B", + "K0215002B", + "K0215005B" + ] }, "K0225002B": { "id": "K0225002B", "unit_obj": "D02004B", "content": "会判断一个函数是否存在反函数.", - "predecessor": [] + "predecessor": [ + "K0225001B", + "K0219003B" + ] }, "K0225003B": { "id": "K0225003B", "unit_obj": "D02004B", "content": "知道反函数与原来函数定义域与值域的关系.", - "predecessor": [] + "predecessor": [ + "K0213006B", + "K0215002B", + "K0215005B" + ] }, "K0225004B": { "id": "K0225004B", "unit_obj": "D02004B", "content": "会根据反函数与原来函数自变量与函数值的关系, 求解反函数或原来函数的自变量或函数值.", - "predecessor": [] + "predecessor": [ + "K0225003B" + ] }, "K0225005B": { "id": "K0225005B", "unit_obj": "D02004B", "content": "会求一个具体函数的反函数.", - "predecessor": [] + "predecessor": [ + "K0225001B", + "K0225002B", + "K0225003B" + ] }, "K0226001B": { "id": "K0226001B", @@ -1046,25 +1278,38 @@ "id": "K0226002B", "unit_obj": "D02004B", "content": "会利用命题``在平面直角坐标系中, 点$P(a,b)$与点$P'(b,a)$关于直线$y=x$成轴对称''证明性质: ``互为反函数的两函数的图像关于$y=x$成轴对称''.", - "predecessor": [] + "predecessor": [ + "K0225001B", + "K0226001B" + ] }, "K0226003B": { "id": "K0226003B", "unit_obj": "D02004B", "content": "能根据性质: ``互为反函数的两函数的图像关于$y=x$成轴对称'', 作出具体函数的反函数的大致图像.", - "predecessor": [] + "predecessor": [ + "K0226002B" + ] }, "K0226004B": { "id": "K0226004B", "unit_obj": "D02004B", "content": "能根据性质: ``互为反函数的两函数的图像关于$y=x$成轴对称''与命题``在平面直角坐标系中, 点$P(a,b)$与点$P'(b,a)$关于直线$y=x$成轴对称'', 求解函数与其反函数的图像上点的相关问题.", - "predecessor": [] + "predecessor": [ + "K0226002B", + "K0226001B" + ] }, "K0226005B": { "id": "K0226005B", "unit_obj": "D02004B", "content": "会探究具体函数与其反函数的基本性质之间的区别与联系.", - "predecessor": [] + "predecessor": [ + "K0225001B", + "K0225003B", + "K0219001B", + "K0217004B" + ] }, "K0226006B": { "id": "K0226006B",