添加一道新题和一个关联题并修改一个题面

题库0.3/Problems.json

@@ -595136,7 +595136,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022789"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -595583,7 +595585,7 @@
     },
     "022470": {
         "id": "022470",
-        "content": "函数 $y=2^{x^2+4 x-5}$ 的严格增区间为\\blank{50}.",
+        "content": "函数 $y=2^{x^2+4 x-5}$ 的单调增区间为\\blank{50}.",
         "objs": [],
         "tags": [],
         "genre": "填空题",
@@ -595593,7 +595595,8 @@
         "usages": [],
         "origin": "2025届高一上学期周末卷13小测",
         "edit": [
-            "20230905\t王伟叶"
+            "20230905\t王伟叶",
+            "20231118\t徐慧"
         ],
         "same": [],
         "related": [],
@@ -603448,6 +603451,49 @@
         "space": "4em",
         "unrelated": []
     },
+    "022788": {
+        "id": "022788",
+        "content": "函数 $y=\\log_{\\frac{1}{2}}(x^2+4 x-5)$ 的单调减区间是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231118\t徐慧"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022789": {
+        "id": "022789",
+        "content": "已知定义在区间 $(-1,1)$ 上的函数 $f(x)=\\dfrac{x+b}{1+x^2}$ 为奇函数.\\\\\n(1) 证明: 函数 $y=f(x)$ 在区间 $(-1,1)$ 上是严格增函数;\\\\\n(2) 解关于 $t$ 的不等式 $f(t-1)+f(t)<0$.",
+        "objs": [],
+        "tags": [],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期周末卷12小测-20231118修改",
+        "edit": [
+            "20230905\t王伟叶",
+            "20231118\t徐慧"
+        ],
+        "same": [],
+        "related": [
+            "022447"
+        ],
+        "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.",