共50条信息
记\(min\{a,b\}=\begin{cases} a\mathrm{{,}}a{\leqslant }b\mathrm{{,}} \\ b\mathrm{{,}}a{ > }b\mathrm{{,}} \end{cases}\)若\(f(x)=min\{x+2,10-x\}(x\geqslant 0)\),则\(f(x)\)的最大值为____\(.\)
\(f\left(x\right)=\begin{cases}2{e}^{x-1},x < 2 \\ {\log }_{3}\left({x}^{2}-1\right),x\geqslant 2\end{cases} \)则\(f(f(2))\)的值为\(——\).
已知函数\(f(x)=\begin{cases}x+2(x\leqslant 0) \\ -x+2(x > 0)\end{cases} \)则\(f(x)\geqslant x^{2}\)的解集为\((\) \()\)
已知\(f(x)=\begin{cases} 2^{x}\mathrm{{-}}3\mathrm{{,}}x{ > }0\mathrm{{,}} \\ g\mathrm{(}x\mathrm{){,}}x{ < }0 \end{cases}\)是奇函数,则\(f(g(-2))=\)
\(.\)设\(f(x)=\begin{cases} 1- \sqrt{x},x\geqslant 0, \\ 2^{x},x < 0, \end{cases}\)则\(f(f(-2))=(\) \()\)
若函数\(f(x)=\left\{\begin{matrix}3x-b(x < 1), \\ 2^{x}(x\geqslant 1)\end{matrix}\right(\quad \quad)\)若\(f(f(\dfrac{5}{6}))=4,\)则\(b=\)____________.
定义\(a*b=\left\{\begin{matrix}a,(a\leqslant b), \\ b,(a > b),\end{matrix}\right(\quad \quad)\)则函数\(f(x)=1*3^{x}\)的值域是__________.
已知函数\(f\left( x \right){=}\begin{cases} {}x{,}x{ > }0 \\ 3^{x}{,}x{\leqslant }0 \end{cases}\),则\(f{[}f\left( \dfrac{1}{2} \right){]}\)的值为__________.
定义在\(R\)上的奇函数\(f(x)\)和定义在\(\left\{ x\left| x\ne 0 \right. \right\}\)上的偶函数\(g(x)\)分别满足\(f(x)=\begin{cases} & {{2}^{x}}-1(0\leqslant x < 1) \\ & \dfrac{1}{x}(x\geqslant 1) \end{cases}\),\(g(x)={{\log }_{2}}x(x > 0)\),若存在实数\(a\),使得\(f(a)=g(b)\)成立,则实数\(b\)的取值范围是( )
进入组卷