收录高二寒假作业8

工具v2/文本文件/新题收录列表.txt

@@ -340,3 +340,6 @@
 20240204-141708 高二寒假作业7
 024501:024502,022875,024503:024512,008994,009009,024513:024514,009070
 
+20240204-142554 高二寒假作业8
+002910,024515:024516,022377,022367,024517,003025,024518:024521,020568,024522,014665,024523:024526
+

题库0.3/Problems.json

@@ -93582,7 +93582,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024521"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -169362,7 +169364,9 @@
             "007972",
             "017589"
         ],
-        "related": [],
+        "related": [
+            "024522"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -228455,7 +228459,9 @@
             "005590",
             "017589"
         ],
-        "related": [],
+        "related": [
+            "024522"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -362014,7 +362020,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024524"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -479966,7 +479974,9 @@
             "007972",
             "005590"
         ],
-        "related": [],
+        "related": [
+            "024522"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -609588,7 +609598,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024523"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -663844,6 +663856,256 @@
         "space": "4em",
         "unrelated": []
     },
+    "024515": {
+        "id": "024515",
+        "content": "已知 $f(x)=\\ln \\dfrac{x+1}{x-1}$, 则 $f^{-1}(2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024516": {
+        "id": "024516",
+        "content": "函数 $f(x)=\\ln (x-2)+\\ln (x+2)$ 的奇偶性是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024517": {
+        "id": "024517",
+        "content": "函数 $y=\\log _{(x+1)}(16-4^x)$ 的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024518": {
+        "id": "024518",
+        "content": "函数 $y=4^x-2^{x+1}-1$, $x \\in[-1,2)$ 的值域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024519": {
+        "id": "024519",
+        "content": "若函数 $f(x)=2^{-|x|}-m$ 与 $x$ 轴有交点, 则实数 $m$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024520": {
+        "id": "024520",
+        "content": "将函数 $y=f(x)$ 的图像沿 $x$ 轴向左平移一个单位, 再沿 $y$ 轴翻折, 得到 $y=\\lg x$ 的图像, 则 $y=f(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024521": {
+        "id": "024521",
+        "content": "已知集合 $A=\\{y | y=(\\dfrac{1}{3})^{|x|}\\}$, $B=\\{a | \\log _a(3 a-1)>0\\}$, 则 $A \\cap \\overline{B}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "002956"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024522": {
+        "id": "024522",
+        "content": "关于 $x$ 方程 $(\\dfrac{1}{2})^x=\\dfrac{2 a+3}{a-5}$ 有负根, 则实数 $a$ 取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "007972",
+            "005590",
+            "017589"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024523": {
+        "id": "024523",
+        "content": "设函数 $f(x)=\\dfrac{x^2+4 x+5}{x^2+4 x+4}$, 作出 $y=f(x)$ 的大致图像, 讨论 $y=f(x)$ 的性质, 并利用性质比较 $f(-\\pi)$ 与 $f(-\\dfrac{\\sqrt{2}}{2})$ 的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "022376"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "024524": {
+        "id": "024524",
+        "content": "(1) 已知关于 $x$ 的方程 $\\lg ^2 x+(m+4) \\lg x+4=0$ 有实数解, 求实数 $m$ 的取值范围;\\\\\n(2) 已知关于 $x$ 的方程 $9^x+(k+4) \\cdot 3^x+4=0$ 有实数解, 求实数 $k$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [
+            "012874"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "024525": {
+        "id": "024525",
+        "content": "已知 $f(x)=\\lg (x+1)$, $g(x)=2 \\lg (2 x+t)$.\\\\\n(1) 若 $t=-1$, 解不等式 $f(x) \\leq g(x)$;\\\\\n(2) 若对任意 $x \\in[0,1)$, 不等式 $f(x) \\leq g(x)$ 恒成立, 求实数 $t$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "024526": {
+        "id": "024526",
+        "content": "设函数 $f(x)=\\log _a(x-3 a)$($a>0$, $a \\neq 1$), 当且仅当点 $P(x, y)$ 是函数 $y=f(x)$ 图像上的点时,点 $Q(x-2 a,-y)$ 是函数 $y=g(x)$ 的图像上的点.\\\\\n(1) 写出函数 $y=g(x)$ 的解析式;\\\\\n(2) 若当 $x \\in[a+2, a+3]$ 时, 恒有 $|f(x)-g(x)| \\leq 1$, 试确定 $a$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240204\t杨懿荔"
+        ],
+        "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.",