共50条信息
已知函数\(f(x+1)=\dfrac{f(x)}{1+f(x)}\),且\(f(1)=1\),则\(f(10)= \)_________.
已知奇函数\(f(x)\),当\(x > 0\)时单调递增,且\(f(1)=0\),若\(f(x-1) > 0\),则\(x\)的取值范围为( )
定义在\(R\)上的奇函数\(f(x)\)满足:对任意\({{x}_{1}},{{x}_{2}}\in \left[ 0,+\infty \right)\),且\({{x}_{1}}\ne {{x}_{2}}\),都有\(({{x}_{1}}-{{x}_{2}})\left[ f({{x}_{1}})-f({{x}_{2}}) \right] > 0\) ,则 \((\) \()\)
已知对于任意的\(x,y > 0\),都有\(f\left( x+1 \right)=f\left( x \right)+f\left( x+2 \right)\),且\(f\left( 1 \right)=1,f\left( 2 \right)=3\),则\(f\left( 2017 \right)=\) \((\) \()\)
函数\(f(x)\)的定义域为\([0,2]\),则函数\(f({{x}^{2}})\)的定义域是( )
设函数\(y=f(x)\)对任意实数\(x,y\)都有\(f(x+y)=f(x)+f(y)+2xy\).
\((\)Ⅰ\()\)若\(f(1)=1\),求\(f(2),f(3),f\left( 4 \right)\)的值;
\((\)Ⅱ\()\)在\((\)Ⅰ\()\)的条件下,猜想\(f(n)(n\in {{N}^{*}})\)的表达式,并用数学归纳法加以证明.
已知\(f(x)\)是定义在\(R\)上的奇函数,且\(f(x+3)=f(x),\)当\(x\in (-2,0)\)时,\(f(x)={{2}^{x}},\)则\(f(2015)+f(2014)+f(2013)=\) .
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