优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知幂函数\(f(x){=}{(m{-}1)}^{2}x^{m^{2}{-}4m{+}2}\)在\((0{,}{+∞})\)上单调递增,函数\(g(x){=}2^{x}{-}t\),对于任意的\(x_{1}{∈[}1{,}6)\),总存在\(x_{2}{∈[}1{,}6)\),使得\(f(x_{1}){=}g(x_{2})\),则\(t\)的取值范围是\((\)  \()\)


              A.\(\varnothing \)  
              B. \(1{\leqslant }t{\leqslant }28\)
              C.\(t{ < }1\)或\(t{ > }28\)           
              D.\(t{\leqslant }1\)或\(t{\geqslant }28\)
            • 2. 已知幂函数\(f(x)\)满足\(f(8)=4\),则\(f\left( \left. \dfrac{ \sqrt{2}}{2} \right. \right)\)________\(f\left( \left. - \dfrac{ \sqrt{3}}{3} \right. \right)(\)填\( > \)、\(=\)或\( < )\).
            • 3.
              幂函数\(f(x)=(m^{2}-2m+1)x^{2m-1}\)在\((0,+∞)\)上为增函数,则实数\(m\)的值为\((\)  \()\)
              A.\(0\)
              B.\(1\)
              C.\(2\)
              D.\(1\)或\(2\)
            • 4.

              已知幂函数\(f\left( x \right)\)过点\(\left( 4,\dfrac{1}{2} \right)\),则\(f\left( x \right)=\)_________ .

            • 5.
              如图所示,\(C_{1}\),\(C_{2}\),\(C_{3}\)为三个幂函数\(y=x^{k}\)在第一象限内的图像,则解析式中指数\(k\)的值依次可以是\((\) \()\)

              A.\(-1\),,\(3\)
              B.\(-1\),\(3\),
              C.,\(-1\),\(3\)
              D.,\(3\),\(-1\)
            • 6.

              下列关于幂函数\(y=x^{α}(α∈Q)\)的论述中,正确的是(    )

              A.当\(α=0\)时,幂函数的图像是一条直线
              B.幂函数的图像都经过\((0,0)\)和\((1,1)\)两个点
              C.若函数\(f(x)\)为奇函数,则\(f(x)\)在定义域内是增函数
              D.幂函数\(f(x)\)的图像不可能在第四象限内
            • 7.

              已知幂函数\(y=f(x)\)的图像过点\((2,\sqrt{2})\),则\(f(9)=\)________.

            • 8.

              已知幂函数\(f\left( x \right)={{x}^{a}}\)的图像经过点\(\left( 2,\dfrac{\sqrt{2}}{2} \right)\),则\(f\left( 4 \right)\)的值等于\((\)   \()\)

              A.\(16\)        
              B.\(\dfrac{1}{16}\)
              C.\(2\)
              D.\(\dfrac{1}{2}\)
            • 9.
              已知幂函数\(y=f(x)\)的图象过点\((3, \sqrt {3})\),则\(f(9)=(\)  \()\)
              A.\(3\)
              B.\(-3\)
              C.\(- \sqrt {3}\)
              D.\( \sqrt {3}\)
            • 10. 幂函数\(y=f(x)\)的图象经过点\((2,8)\),则满足\(f(x)=27\)的\(x\)的值是 ______ .
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