共50条信息
定义域为\(R\)的偶函数\(f\left(x\right) \)满足对任意的\(x∈R \)，有\(f\left(x+2\right)=f\left(x\right)+f\left(1\right) \)且当\(x∈\left[2,3\right] \)时，\(f\left(x\right)=-2{x}^{2}+12x-18 \) ，若函数\(y=f\left(x\right)-{\log }_{a}\left(\left|x\right|+1\right) \)在\(R\)上恰有六个零点，则实数\(a\)的取值范围是\((\) \()\)
设函数\(f(x)\)为定义域为\(R\)的奇函数，且\(f(x)=f(2-x)\)，当\(x∈[0,1]\)时，\(f(x)=\sin x\)，则函数\(g(x)=|\cos (πx)|-f(x)\)在区间\([-\dfrac{5}{2},\dfrac{9}{2}]\)上的所有零点的和为
已知\(f(x)\)是定义在\(R\)上的周期为\(2\)的函数，当\(x∈(-1,1]\)时，\(f(x)=\begin{cases} -4x^{2}+ \dfrac{9}{8},-1 < x\leqslant 0, \\ \log _{2}x,0 < x\leqslant 1, \end{cases}\)，则\(f(f( \dfrac{7}{2}))=\)________．
已知\(f_{1}(x)=\sin x+\cos x\)，\(f_{n+1}(x)\)是\(f_{n}(x)\)的导函数，即\(f_{2}(x)=f_{1}′(x)\)，\(f_{3}(x)=f_{2}′(x)\)，\(…\)，\(f_{n+1}(x)=f_{n}′(x)\)，\(n∈N^{*}\)，则\(f_{2017}(x)=(\) \()\)
已知函数\(f(x)\)的定义域为\(R{.}\)当\(x{ < }0\)时，\(f(x){=}x^{3}{-}1\)；当\({-}1{\leqslant }x{\leqslant }1\)时，\(f({-}x){=-}f(x)\)；当\(x{ > }\dfrac{1}{2}\)时，\(f(x{+}\dfrac{1}{2}){=}f(x{-}\dfrac{1}{2}){.}\)则\(f(6){=}({ })\)
已知\(
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
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