优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知定义在\(R\)上的偶函数\(f\left( x \right)\)满足\(f\left( x+4 \right)=f\left( x \right)\),且当\(0\leqslant x\leqslant 2\)时,\(f\left( x \right)=\min \left\{ -{{x}^{2}}+2x,2-x \right\}\),若方程\(f\left( x \right)-mx=0\)恰有两个根,则\(m\)的取值范围是

              A.\((-\infty ,-\dfrac{1}{3})\bigcup (\dfrac{1}{3},{+}\infty )\)
              B.\((-\infty ,-\dfrac{1}{3}]\bigcup [\dfrac{1}{3},{+}\infty )\) 
              C.\((-2,-\dfrac{1}{3})\bigcup (\dfrac{1}{3},2)\)
              D.\([-2,-\dfrac{1}{3}]\bigcup [\dfrac{1}{3},2]\)
            • 2.

              函数\(f(x){=}(\dfrac{1}{3})^{x}{+}\dfrac{1}{\sqrt{x{+}3}}{-}3\)的零点所在区间是\(({  })\)

              A.\((1{,}2)\)
              B.\((0{,}1)\)
              C.\(({-}1{,}0)\)
              D.\(({-}2{,}{-}1)\)
            • 3.

              已知\(y=f(x)\)为\(R\)上的连续可导函数,且\(xf{{"}}(x)+f(x) > 0\),则函数\(g(x)=xf(x)+1(x > 0)\)的零点个数为(    )

              A.\(0\)
              B.\(1\)
              C.\(2\)
              D.不能确定
            • 4. 已知函数\(f(x)= \dfrac {6}{x}-\log _{2}x\),则在下列区间中,函数\(f(x)\)有零点的是\((\)  \()\)
              A.\((0,1)\)
              B.\((1,2)\)
              C.\((2,4)\)
              D.\((4,+∞)\)
            • 5.

              函数\(f(x)=\dfrac{4}{x}-{{2}^{x}}\)的零点所在区间是

              A.\((0,\dfrac{1}{2})\)
              B.\((\dfrac{1}{2},1)\)                                          
              C.\((1,\dfrac{3}{2})\)
              D.\((\dfrac{3}{2},2)\)
            • 6.

              函数\(f(x){=}(\dfrac{1}{2})^{x}{-}\log_{2}x\)的零点个数为\((\)  \()\)

              A.\(0\)                                
              B.\(1\)                                
              C.\(2\)                                
              D.\(3\)
            • 7.

              已知函数\(f(x)=\sin ωx- \sqrt{3}\cos ωx(ω > 0)\)在\((0,π)\)上有且只有两个零点,则实数\(ω\)的取值范围为\((\)  \()\)

              A.\(\left( \left. 0, \dfrac{4}{3} \right. \right]\)
              B.\(\left( \left. \dfrac{4}{3}, \dfrac{7}{3} \right. \right] \)

              C.\(\left( \left. \dfrac{7}{3}, \dfrac{10}{3} \right. \right]\)
              D.\(\left( \left. \dfrac{10}{3}, \dfrac{13}{3} \right. \right] \)
            • 8.
              若函数\(f(x)=m+\log _{2}x(x\geqslant 1)\)存在零点,则实数\(m\)的取值范围是\((\)  \()\)
              A.\((-∞,0]\)
              B.\([0,+∞)\)
              C.\((-∞,0)\)
              D.\((0,+∞)\)
            • 9.
              若函数 \(f\)\(( \)\(x\)\()\)图象是连续不断的,且 \(f\)\((0) > 0\), \(f\)\((1)·\) \(f\)\((2)·\) \(f\)\((4) < 0\),则下列命题正确的是(    )
              A.函数 \(f\)\(( \)\(x\)\()\)在区间\((0,1)\)内有零点  
              B.函数 \(f\)\(( \)\(x\)\()\)在区间\((1,2)\)内有零点
              C.函数 \(f\)\(( \)\(x\)\()\)在区间\((0,2)\)内有零点  
              D.函数 \(f\)\(( \)\(x\)\()\)在区间\((0,4)\)内有零点
            • 10.

              若函数\(f(x)=2mx+4\)在\(\left[-2,1\right] \)上存在零点,则实数\(m\)的取值范围是          (    )

              A.\(\left[- \dfrac{5}{2},4\right] \)
              B.\((-∞,-2]∪[1,+∞) \)
              C.\(\left[-1,2\right] \)
              D.\(\left(-2,1\right) \)
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