From fe49d75a1357da7aa8adcc10065d4110104c65e4 Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Mon, 8 Jan 2024 11:02:43 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A526=E5=B1=8A=E9=AB=98=E4=B8=80?=
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MIME-Version: 1.0
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---
 题库0.3/Problems.json | 411 +++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 405 insertions(+), 6 deletions(-)

diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index e008ec95..3a9a97cd 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -43123,7 +43123,8 @@
         ],
         "same": [],
         "related": [
-            "006445"
+            "006445",
+            "023461"
         ],
         "remark": "",
         "space": "4em",
@@ -161896,7 +161897,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023447"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -224847,7 +224850,8 @@
         ],
         "same": [],
         "related": [
-            "011960"
+            "011960",
+            "023452"
         ],
         "remark": "",
         "space": "4em",
@@ -330558,7 +330562,8 @@
         "related": [
             "007909",
             "009523",
-            "010180"
+            "010180",
+            "023452"
         ],
         "remark": "",
         "space": "4em",
@@ -536424,7 +536429,9 @@
         "same": [
             "007820"
         ],
-        "related": [],
+        "related": [
+            "023451"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -539685,7 +539692,9 @@
             "20221223\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023451"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -626621,6 +626630,396 @@
         "space": "4em",
         "unrelated": []
     },
+    "023444": {
+        "id": "023444",
+        "content": "函数 $y=\\dfrac{(x+1)^0}{\\sqrt{|x|-x}}$ 的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023445": {
+        "id": "023445",
+        "content": "函数 $y=\\sqrt{\\dfrac{2+x}{1-x}}+\\sqrt{x^2-x-2}$ 的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023446": {
+        "id": "023446",
+        "content": "设函数 $f(x)=\\begin{cases}\\sqrt{x-1},&  x \\geq 1,\\\\1,&  x<1,\\end{cases}$ 则 $f(f(f(2)))=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023447": {
+        "id": "023447",
+        "content": "已知 $f(x)$ 是奇函数, 当 $x<0$ 时, $f(x)=x(x-1)$, 则 $f(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "005361"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023448": {
+        "id": "023448",
+        "content": "函数 $f(x)=\\dfrac{1}{x}$ 的严格减区间是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023449": {
+        "id": "023449",
+        "content": "已知 $a$ 是常数, 函数 $y=|x-a|$ 在 $[2,+\\infty)$ 上是严格增函数, 则 $a$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023450": {
+        "id": "023450",
+        "content": "已知 $a$ 是常数, $f(x)$ 是定义在 $\\mathbf{R}$ 上的偶函数, 它在 $[0,+\\infty)$ 上是严格减函数, 则 $f(-0.74)$ 与 $f(a^2-a+1)$ 的大小关系是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023451": {
+        "id": "023451",
+        "content": "若 $0<x<\\dfrac{1}{2}$, 则函数 $y=x(1-2 x)$ 的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020200",
+            "020327"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023452": {
+        "id": "023452",
+        "content": "函数 $y=\\dfrac{2}{x-1}$ 在区间 $[2,6]$ 上的最大值与最小值的和等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "007909",
+            "011960"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023453": {
+        "id": "023453",
+        "content": "设 $y=f(x)$ 是定义在 $\\mathbf{R}$ 上的奇函数, 则一定在 $y=f(x)$ 图像上的点是\\bracket{20}.\n\\fourch{$(-a,-f(-a))$}{$(a, f(-a))$}{$(a,-f(a))$}{$(-a,-f(a))$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023454": {
+        "id": "023454",
+        "content": "函数 $y=1-\\dfrac{1}{x-1}$\\bracket{20}.\n\\twoch{在 $(-1,+\\infty)$ 上严格增}{在 $(-1,+\\infty)$ 上严格减}{在 $(1,+\\infty)$ 上严格增}{在 $(1,+\\infty)$ 上严格减}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023455": {
+        "id": "023455",
+        "content": "在边长为 $4$ 的正方形 $ABCD$ 的边上有动点 $P$, 从 $B$ 点开始, 沿折线 $BCDA$ 向 $A$ 点运动,设点 $P$ 移动的路程为 $x$, $\\triangle ABP$ 面积为 $S$.\\\\\n(1) 求函数 $S=f(x)$ 的解析式、定义域和值域;\\\\\n(2) 求 $f[f(3)]$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023456": {
+        "id": "023456",
+        "content": "作出函数 $y=\\sqrt{-x^2+4 x-3}$ 的大致图像, 并写出其定义域、值域、及单调区间(含每个单调区间上的单调性).",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023457": {
+        "id": "023457",
+        "content": "已知 $f(\\dfrac{x+1}{x})=\\dfrac{x^2+1}{x^2}+\\dfrac{1}{x}$, 则 $f(3)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023458": {
+        "id": "023458",
+        "content": "设 $f(x)=\\dfrac{x}{x^2+a}$ 在区间 $[3,+\\infty)$ 上是严格减函数, 则正常数 $a$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023459": {
+        "id": "023459",
+        "content": "设 $f(x+1)=x^2-2 x-7$, $x \\in[t-1, t]$, 其中 $t \\in \\mathbf{R}$, 则函数 $f(x)$ 的最小值 $g(t)$ 的解析式为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023460": {
+        "id": "023460",
+        "content": "设函数 $f(x)=\\dfrac{a x^2+1}{b x+c}$ 是奇函数 ($a, b, c \\in \\mathbf{Z}$), 且 $f(1)=2$, $f(2)<3$.\\\\\n(1) 求 $a, b, c$ 的值;\\\\\n(2) 判断并证明 $f(x)$ 在 $[1,+\\infty)$ 上的单调性.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023461": {
+        "id": "023461",
+        "content": "求函数 $y=2 x+\\sqrt{1-x^2}$ 的最大值与最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001283"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023462": {
+        "id": "023462",
+        "content": "已知定义在 $\\mathbf{R}$ 上的函数 $y=f(x)$ 满足: 对任意 $x \\in \\mathbf{R}$, 总成立 $f(x+1)=2 f(x)$, 且 $y=f(x)$ 的值域是 $(0,+\\infty)$ 的子集.\\\\\n(1) 试举出一个满足条件的函数 $y=f(x)$ 的例子;\\\\\n(2) 满足条件的函数一定是增函数吗? 说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",