收录高三寒假作业46新题

工具v2/文本文件/新题收录列表.txt

@@ -136,3 +136,6 @@
 20240125-123757
 023960:023965
 
+20240125-125210
+023966:023969,000724,023970
+

题库0.3/Problems.json

@@ -360399,7 +360399,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023970"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -436772,7 +436774,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023969"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -607259,7 +607263,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023970"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -645984,6 +645990,111 @@
         "space": "4em",
         "unrelated": []
     },
+    "023966": {
+        "id": "023966",
+        "content": "函数 $f(x)=x+\\dfrac{1}{x}+1$, $f(a)=3$, 则 $f(-a)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023967": {
+        "id": "023967",
+        "content": "设函数 $f(x)$ 是定义在 $\\mathbf{R}$ 上的奇函数, 且 $f(x)=\\begin{cases}\\log _2(x+1),&  x \\geq 0,\\\\g(x),&  x<0,\\end{cases}$ 则 $f(-7)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023968": {
+        "id": "023968",
+        "content": "已知函数 $f(x)$ 是周期为 $2$ 的奇函数, 当 $x \\in[0,1)$ 时, $f(x)=\\lg (x+1)$, 则 $f(\\dfrac{2016}{5})+\\lg 18=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023969": {
+        "id": "023969",
+        "content": "设函数 $f(x)$ 是定义在 $\\mathbf{R}$ 上周期为 $2$ 的偶函数, 若当 $x \\in[0,1]$ 时, $f(x)=x+1$, 则 $f(\\dfrac{3}{2})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "015776"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023970": {
+        "id": "023970",
+        "content": "函数 $f(x)$ 的定义域为 $D=\\{x | x \\neq 0\\}$, 且满足对于任意 $x_1$、$x_2\\in D$, 有 $f(x_1\\cdot x_2)=f(x_1)+f(x_2)$.\\\\\n(1) 求 $f(1)$ 的值;\\\\\n(2) 判断 $f(x)$ 的奇偶性并证明你的结论;\\\\\n(3) 如果 $f(4)=1$, $f(x-1)<2$, 且 $f(x)$ 在 $(0,+\\infty)$ 上是严格增函数, 求 $x$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "012880",
+            "022466"
+        ],
+        "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.",