数学试题识别

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        "detected_text": "f ( x ) = \\frac { a x + 1 } { x + 2 }  "
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      {
        "detected_text": "\\frac { f ( x _ { 1 } ) - f ( x _ { 2 } ) } { x _ { 1 } - x _ { 2 } } &lt 0  "
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        "detected_text": "C . \\quad \\lbrack \\frac { 1 } { 3 } , \\frac { 1 } { 2 } )  "
      },
      {
        "detected_text": "A . \\quad ( 0 , \\frac { 1 } { 2 } )  "
      },
      {
        "detected_text": "D . \\quad ( \\frac { 1 } { 2 } , 1 )  "
      },
      {
        "detected_text": "C . \\quad \\lbrack \\frac { 1 } { 4 } , 1 )  "
      },
      {
        "detected_text": "A . \\quad ( 0 , \\frac { 1 } { 4 } \\rbrack  "
      },
      {
        "detected_text": "f ( x ) = \\left\\lbrace\\begin{array}{l} { a ^ { x } , } & { x &lt 0 } \\\\ { ( a - 3 ) x + 4 a , x \\geq 0 } \\end{array}\\right.  "
      },
      {
        "detected_text": "f ( x ) = \\left\\lbrace\\begin{array}{l} { ( 2 a - 1 ) x + a , x \\geq 1 } \\\\ { \\log _ a x } & { x &lt 1 } \\end{array}\\right.  "
      },
      {
        "detected_text": "B . \\quad ( 0 , \\frac { 1 } { 3 } \\rbrack  "
      },
      {
        "detected_text": "x _ { 1 } \\neq x _ { 2 }  "
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        "detected_text": "题型4:已知函数的单调性求参数的取值范围"
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      {
        "detected_text": "[例9] (★★★) 已知函数"
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      {
        "detected_text": "在区间(-2, +∞)上是增函数,试求a的取值范围."
      },
      {
        "detected_text": "[例10] (★★★★) 已知函数,若"
      },
      {
        "detected_text": "在(0, +∞)上单调递减，则a的取"
      },
      {
        "detected_text": "值范围为( )"
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      {
        "detected_text": "[例11] (★★★★★)设 "
      },
      {
        "detected_text": "，对任意的."
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      {
        "detected_text": "都有"
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      {
        "detected_text": "成立，"
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      {
        "detected_text": "则a的取值范围是( )"
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      {
        "detected_text": "B. (0, 1)"
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        "detected_text": "D. (0,3)"
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      {
        "detected_text": "2019年高三.数学.寒假文科 "
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        "detected_text": ""
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        "detected_text": ""
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            "question_text_no": "",
            "question_text_type": 3,
            "question_text": "题型4:已知函数的单调性求参数的取值范围",
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            "question_text_no": "[例9]",
            "question_text_type": 3,
            "question_text": "(★★★)已知函数f(x)=\\frac{ax+1}{x+2}在区间(-2,+∞)上是增函数,试求a的取值范围.",
            "question_options": "[{\"option\":[]}]",
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            "question_text_no": "[例10]",
            "question_text_type": 1,
            "question_text": "(★★★★)已知函数,若f(x)=\\left\\lbrace\\begin{array}{l}{(2a-1)x+a,x\\geq1}\\\\{\\log_ax}&{x&lt1}\\end{array}\\right.在(0,+∞)上单调递减，则a的取值范围为##{()}##",
            "question_options": "[{\"option\":[\"$${\\\\quad(0,\\\\frac{1}{2})}$$\",\"$${\\\\quad(0,\\\\frac{1}{3}\\\\rbrack}$$\",\"$${\\\\quad\\\\lbrack\\\\frac{1}{3},\\\\frac{1}{2})}$$\",\"$${\\\\quad(\\\\frac{1}{2},1)}$$\"]}]",
            "question_sub_question": "[]"
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            "question_text_no": "[例11]",
            "question_text_type": 1,
            "question_text": "(★★★★★)设f(x)=\\left\\lbrace\\begin{array}{l}{a^{x},}&{x&lt0}\\\\{(a-3)x+4a,x\\geq0}\\end{array}\\right.，对任意的.x_{1}\\neqx_{2}都有\\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}&lt0成立，则a的取值范围是##{()}##",
            "question_options": "[{\"option\":[\"$${\\\\quad(0,\\\\frac{1}{4}\\\\rbrack}$$\",\"(0,1)\",\"$${\\\\quad\\\\lbrack\\\\frac{1}{4},1)}$$\",\"(0,3)\"]}]",
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