f(x+2)+f(x-2)=f(x) f(0)=5求 f(18)
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f(x+2)+f(x-2)=f(x) f(0)=5求 f(18)
f(x+2)+f(x-2)=f(x) f(0)=5求 f(18)
f(x+2)+f(x-2)=f(x) f(0)=5求 f(18)
∵f(0)=5
∵f(x)=f(x+2)+f(x-2)
∴f(x+2)=f(x)-f(x-2)
∴f(x+2)=f(x+2+2)+f(x+2-2)=f(x+4)+f(x)=f(x)-f(x-2)
∵f(x+4)+f(x)=f(x)-f(x-2)
∴f(x+4)=-f(x-2)
∵f(x+2+4)=-f(x+2-2)
∴f(x+6)= -f(x)
∵f(x+6+6)=-f(x+6)=-(-f(x))= f(x)
∴f(x+12)=f(x)
∵f(x+6+12)=f(x+6)= -f(x)
∴f(x+18)= -f(x)
f(18)=f(18+0)=-f(0)=-5
f(x+2)+f(x-2)=f(x)
f(x+2)=f(x)-f(x-2)
f(x+4)=f(x+2)-f(x)=-f(x-2)
f(x+6)=f(x+4)-f(x+2)=f(x+2)-f(x)-f(x+2)=-f(x)
f(x+12)=-f(x+6)=f(x) 周期为12
f(18)=f(6+12)=f(6)=-f(0)=-5
f(x+2)=f(x)-f(x-2)
f(x)=f(x-2)-f(x-4)
两式相减得
f(x+2)=-f(x-4),即f(x)=-f(x-6)
所以f(18)=-f(12)=f(6)=-f(0)=-5
f(X)=f(X+2)(x
f(x+2)>=f(x)+2,f(x+3)
f(x+2)+f(x-2)=f(x) f(0)=5求 f(18)
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