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            • 1.

              若幂函数\(f(x)=mx^{a}\)的图像经过点\(A\left( \dfrac{1}{4},\dfrac{1}{2} \right)\),则它在点\(A\)处的切线方程是________.

            • 2.

              已知函数\(f(x)=(m^{2}-m-5)x^{m}\)是幂函数,且在\(x∈(0,+∞)\)上为增函数,则实数\(m\)的值是\((\)  \()\)

              A.\(-2\)                           
              B.\(4\)

              C.\(3\)                                                      
              D.\(-2\)或\(3\)
            • 3.

              已知函数\(f(x)=x{\,\!}^{ \frac{1}{2}} \),则\((\)  \()\)

              A.\(∃x_{0}∈R\),\(f(x_{0}) < 0\)

              B.\(∀x∈[0,+∞)\),\(f(x)\geqslant 0\)

              C.\(∃x_{1}\),\(x_{2}∈[0,+∞)\),\( \dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0\)

              D.\(∀x_{1}∈[0,+∞)\),\(∃x_{2}∈[0,+∞)\),\(f(x_{1}) > f(x_{2})\)
            • 4.

              幂函数的图像过点\(\left( \dfrac{1}{2}, \dfrac{1}{4}\right) \),则它的单调递减区间是________________ .

            • 5.

              已知函数\(f\left( x \right)=\left( {{m}^{2}}-m-1 \right){{x}^{4{{m}^{9}}-{{m}^{5}}-1}}\)是幂函数,对任意的\({{x}_{1}},{{x}_{2}}\in \left( 0,+\infty \right)\),且\({{x}_{1}}\ne {{x}_{2}}\),\(\left( {{x}_{1}}-{{x}_{2}} \right)\left[ f\left( {{x}_{1}} \right)-f\left( {{x}_{2}} \right) \right] > 0\),若\(a,b\in R\),且\(a+b > 0,ab < 0\),则\(f\left( a \right)+f\left( b \right)\)的值\((\)  \()\)

              A.恒大于\(0\)   
              B.恒小于\(0\)   
              C.等于\(0\)   
              D.无法判断
            • 6.

              已知\(a={{2}^{\frac{4}{3}}}\),\(b={{3}^{\frac{2}{3}}}\),\(c={{25}^{\frac{1}{3}}}\),则\((\)   \()\)

              A.\(b < a < c\)
              B.\(a < b < c\)
              C.\(b < c < a\)
              D.\(c < a < b\)
            • 7. 已知\(f(x)=(m^{2}-m-1)x^{-5m-1}\)是幂函数,且在区间\((0,+∞)\)上单调递增.
              \((\)Ⅰ\()\)求\(m\)的值;
              \((\)Ⅱ\()\)解不等式\(f(x-2) > 16\).
            • 8.

              设函数\(y={{x}^{3}}\)与\(y={{\left( \dfrac{1}{2} \right)}^{x-2}}\)的图象的交点为\(\left({x}_{0},{y}_{0}\right) \),则\({{x}_{0}}\)所在的区间是      (    )

              A.\(\left(0,1\right) \)                   
              B.\(\left(1,2\right) \)                  
              C.\(\left(2,3\right) \)             
              D.\(\left(3,4\right) \)
            • 9.

              在同一坐标系内,函数\(y=x^{a}(a\neq 0)\)和\(y=ax+\dfrac{1}{a}\)的图象可能是________\((\)填序号\()\).

            • 10.

              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\(2\)
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