共50条信息
幂函数\(f(x)=({{m}^{2}}-2m+1){{x}^{2m-1}}\)在\((0,+\infty )\)上为增函数,则实数\(m\)的值为\((\) \()\)
若幂函数\(f(x)={{x}^{a}}\)的图像经过点满足\(\left( {} \right.2,\dfrac{1}{4}\left. {} \right)\),则\(a\)的值是______________.
已知\(a={{\left( \dfrac{1}{3} \right)}^{\frac{2}{3}}},b={{\left( \dfrac{1}{4} \right)}^{\frac{1}{3}}},c=\log _{3}^{\pi }\),则\(a,b,c\)的大小关系为__________\(.(\)用“\( < \)”号连接\()\).
已知函数\(f(x)=(2m^{2}-6m+5)x^{m+1}\)为幂函数且为偶函数.
\((1)\)求\(f(x)\)的解析式;
\((2)\)若函数\(y=f(x)-2(a-1)x+1\)在区间\((2,3)\)上为单调函数,求实数\(a\)的取值范围.
已知集合 \(A=\left\{ x\left| y=\lg \left( 2-x \right) \right. \right\}\) ,集合\(B=\left\{ y\left| y=\sqrt{x} \right. \right\}\),则\(A\bigcap B{=}\) .
函数\(f\left( x \right)=\left( {{m}^{2}}-m-1 \right){{x}^{{{m}^{2}}+m-1}}\)是幂函数,且在\(\left( 0,+\infty \right)\)上是减函数,则实数\(m\)为( )
抛物线\(y^{2}=8x\)与曲线\(xy=k(k > 0)\)交于点\(M\),若\(M\)到抛物线焦点\(F\)的距离为\(4\),则\(k=\) .
已知\(a{=}(\sqrt{2})^{\frac{4}{3}}\),\(b{=}2^{\frac{2}{5}}\),\(c{=}9^{\frac{1}{3}}\),则\((\) \()\)
如图的曲线是幂函数\(y=x^{n}\)在第一象限内的图象\(.\)已知\(n\)分别取\(±2\),\(\pm \dfrac{1}{2}\)四个值,与曲线\(c_{1}\)、\(c_{2}\)、\(c_{3}\)、\(c\)相应的\(n\)依次为\((\) \()\)
已知\(n∈\{-2,-1,0,1,2,3\}\),若\({{(-\dfrac{1}{2})}^{n}} > {{(-\dfrac{1}{3})}^{n}}\),则\(n=\)________.
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