共50条信息
下列函数的最小值为\(2\)的是 ( )
设\(f\left(x\right)=\begin{cases}{\left(x-a\right)}^{2},x\leqslant 0 \\ x+ \dfrac{1}{x}+a+4,x > 0\end{cases} \),若\(f\left(0\right) \)是\(f\left(x\right) \)的最小值,则\(a\)的取值范围为( )
函数\(f(x)=\dfrac{{x}^{2}+x+1}{2x+1},(x\geqslant 1) \)的最小值是________
对任意实数\(x \)均有\({e}^{2x}-\left(a-3\right){e}^{x}+4-3a > 0 \),则实数\(a \)的取值范围为__________\(.\)
已知函数\(f(x)=x+\dfrac{4}{x}\),\(g(x)={{2}^{x}}+a\),若\(\forall {{x}_{1}}\in \left[ \dfrac{1}{2},1 \right],\exists {{x}_{2}}\in \left[ 2,3 \right],\)使得\(f\left( {{x}_{1}} \right)\geqslant g\left( {{x}_{2}} \right)\),则实数\(a\)的取值范围是________.
已知函数\(f(x)=\begin{cases}\left|{\log }_{2}\left(-x\right)\right|,x < 0 \\ {x}^{2}-2x+2,x\geqslant 0\end{cases} \),函数\(F(x)=f(x)-a\)有四个不同的零点\(x_{1}\),\(x_{2}\),\(x_{3}\),\(x_{4}\)且满足:\(x_{1} < x_{2} < x_{3} < x_{4}\),则\(\dfrac{{{x}_{{2}}}}{{{x}_{{1}}}}+\dfrac{{{x}_{{3}}}x_{{1}}^{{2}}+{{x}_{{4}}}x_{{1}}^{{2}}}{{2}}\)的取值范围为________.
若函数\(f(x)= \dfrac{(2+m)x}{{x}^{2}-m} \)的图象如图所示,则\(m\)的范围为( )
对任意实数\(x \)均有\({e}^{2x}-(a-3){e}^{x}+4-3a > 0 \),则实数\(a \)的取值范围为__________.
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