1、对任意实数x,y.均满足f(x+y^2)=f(x)+2[f(y)]^2且f(1)不等于0.则f(2009)等于?2、已知函数f(x)满足:对一切实数x,y恒有f(x+y)-f(y)=(x+2y+1)x,且f(1)=0 求(1)f(0)的值 (2)若一切x属于(0,1/2)不等式f(x)+2
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![1、对任意实数x,y.均满足f(x+y^2)=f(x)+2[f(y)]^2且f(1)不等于0.则f(2009)等于?2、已知函数f(x)满足:对一切实数x,y恒有f(x+y)-f(y)=(x+2y+1)x,且f(1)=0 求(1)f(0)的值 (2)若一切x属于(0,1/2)不等式f(x)+2](/uploads/image/z/8318828-20-8.jpg?t=1%E3%80%81%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%2Cy.%E5%9D%87%E6%BB%A1%E8%B6%B3f%28x%2By%5E2%29%3Df%28x%29%2B2%5Bf%28y%29%5D%5E2%E4%B8%94f%281%29%E4%B8%8D%E7%AD%89%E4%BA%8E0.%E5%88%99f%282009%29%E7%AD%89%E4%BA%8E%3F2%E3%80%81%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%3A%E5%AF%B9%E4%B8%80%E5%88%87%E5%AE%9E%E6%95%B0x%2Cy%E6%81%92%E6%9C%89f%28x%2By%29-f%28y%29%3D%28x%2B2y%2B1%29x%2C%E4%B8%94f%281%29%3D0+%E6%B1%82%EF%BC%881%EF%BC%89f%280%29%E7%9A%84%E5%80%BC+%282%29%E8%8B%A5%E4%B8%80%E5%88%87x%E5%B1%9E%E4%BA%8E%EF%BC%880%2C1%2F2%EF%BC%89%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%2B2)
1、对任意实数x,y.均满足f(x+y^2)=f(x)+2[f(y)]^2且f(1)不等于0.则f(2009)等于?2、已知函数f(x)满足:对一切实数x,y恒有f(x+y)-f(y)=(x+2y+1)x,且f(1)=0 求(1)f(0)的值 (2)若一切x属于(0,1/2)不等式f(x)+2
1、对任意实数x,y.均满足f(x+y^2)=f(x)+2[f(y)]^2且f(1)不等于0.则f(2009)等于?
2、已知函数f(x)满足:对一切实数x,y恒有f(x+y)-f(y)=(x+2y+1)x,且f(1)=0 求(1)f(0)的值 (2)若一切x属于(0,1/2)不等式f(x)+2
1、对任意实数x,y.均满足f(x+y^2)=f(x)+2[f(y)]^2且f(1)不等于0.则f(2009)等于?2、已知函数f(x)满足:对一切实数x,y恒有f(x+y)-f(y)=(x+2y+1)x,且f(1)=0 求(1)f(0)的值 (2)若一切x属于(0,1/2)不等式f(x)+2
1.
(1) 代入x=1,y=0,得f(1)=f(1)+f(0),解得f(0)=0;
(2) 代入x=0,y=1,得f(1)=f(0)+2[f(1)]^2,解得f(1)=0.5;
(3) 所以f(2009) = f(2008+1^2) = f(2008)+2[f(1)]^2 = f(2008)+0.5;
= f(2007)+0.5+0.5 = ...= f(1)+2008*0.5 = 1004.5
2.
(1) 代入x=1,y=0,得f(1)-f(0)=2,因f(1)=0,解得f(0)=-2;
(2) 先求f(x)的表达式,代入y=0,得f(x)-f(0)=(x+1)x,因f(0)=-2,故
f(x)=(x+1)x-2;
(3) (0,1/2)时,f(x)+2
1 当x=1,y=0时可得f(1)=f(1)+2[f(0)]^2
f(0)=0
当x=0,y=1时,f(1)=f(0)+2[f(1)]^2=2[f(1)]^2
f(1)=1/2
当x=1,y=1时,f(2)=f(1)+2[f(1)]^2=1
f(3)=f(2+1...
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1 当x=1,y=0时可得f(1)=f(1)+2[f(0)]^2
f(0)=0
当x=0,y=1时,f(1)=f(0)+2[f(1)]^2=2[f(1)]^2
f(1)=1/2
当x=1,y=1时,f(2)=f(1)+2[f(1)]^2=1
f(3)=f(2+1)=f(2)+2[f(1)]^2=1+1/2=3/2
f(4)=......4/2
......
f(2009)=2009/2
2 1 当x=1,y=0时,f(1)-f(0)=2
因为f(1)=0
所以f(0)=-2
2
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