(1)若函数f(x)在R上恒有f(x)=f(x+1)+f(x-1),且f(1)=2,求f(2014)的值(2)已知函数f(x)满足f(x+1)=[1+f(x)]/[1-f(x)],若f(0)=2010,求f(2014).
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(1)若函数f(x)在R上恒有f(x)=f(x+1)+f(x-1),且f(1)=2,求f(2014)的值(2)已知函数f(x)满足f(x+1)=[1+f(x)]/[1-f(x)],若f(0)=2010,求f(2014).
(1)若函数f(x)在R上恒有f(x)=f(x+1)+f(x-1),且f(1)=2,求f(2014)的值
(2)已知函数f(x)满足f(x+1)=[1+f(x)]/[1-f(x)],若f(0)=2010,求f(2014).
(1)若函数f(x)在R上恒有f(x)=f(x+1)+f(x-1),且f(1)=2,求f(2014)的值(2)已知函数f(x)满足f(x+1)=[1+f(x)]/[1-f(x)],若f(0)=2010,求f(2014).
(1)
f(x+1)=f(x)-f(x-1)
=[f(x-1)-f(x-2)]-f(x-1)
=-f(x-2)
∴f(x)=-f(x-3)=f(x-6)
f(2014)=f(6*335+4)
=f(4)
=-f(1)
=-2
(2)
f(x+1)=[1+f(x)]/[1-f(x)]
=[1+[1+f(x-1)]/[1-f(x-1)]]/[1-[1+f(x-1)]/[1-f(x-1)]]
=2/[-2f(x-1)]
=-1/f(x-1)
∴f(x)=-1/f(x-2)
=f(x-4)
∴f(2014)=f(4*503+2)
=f(2)
=-1/f(0)
=-1/2010
如仍有疑惑,欢迎追问.
(1)
f(x+1)=f(x)-f(x-1)
=[f(x-1)-f(x-2)]-f(x-1)
=-f(x-2)
∴f(x)=-f(x-3)=f(x-6)
f(2014)=f(6*335+4)
=f(4)
=-f(1)
=-2
(2)
f(x+1)=[1+f(x)]/[1-f(x)]
=[1+[1+f(...
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(1)
f(x+1)=f(x)-f(x-1)
=[f(x-1)-f(x-2)]-f(x-1)
=-f(x-2)
∴f(x)=-f(x-3)=f(x-6)
f(2014)=f(6*335+4)
=f(4)
=-f(1)
=-2
(2)
f(x+1)=[1+f(x)]/[1-f(x)]
=[1+[1+f(x-1)]/[1-f(x-1)]]/[1-[1+f(x-1)]/[1-f(x-1)]]
=2/[-2f(x-1)]
=-1/f(x-1)
∴f(x)=-1/f(x-2)
=f(x-4)
∴f(2014)=f(4*503+2)
=f(2)
=-1/f(0)
=-1/2010
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