Question

f(x+3=+f(x-1),+f(1)=2,求f(101)

Answer 1

问：f(x+3=+f(x-1),+f(1)=2,求f(101)

问：f（x+3）= f（x-1）, f（1）=2,求f（101）

答：亲，很高兴为您解答f(x+3=+f(x-1),+f(1)=2,求f(101)问题：解题思路如下

答：解：x = 100

答：f(x+3) = f(103) = f(100+3) = f(x-1) = f(99)

答：f(99) = f(100-1) = f(x) = f(100)

答：f(x) = f(100) = 2

答：f(101) = f(102) = f(100+2) = f(x+2)

答：f(x+2) = f(100+2) = f(102) = 2

答：故：f(101)=2

问：为什么f（x）= f（100)=2

答：更详细的解答：令y=x+3 （1）得 y-1 = x （2）由题设得：f(1)=2根据(2)得：f(y-1) = f(x)由(1)得：f(x+3) = f(y)即有: f(x+3)=f(y-1)将x=1代入得f(1+3)=f(1-1)即有：f(4)=f(0)同理可得:f(5)=f(1)f(6)=f(2)......f(99)=f(95)f(100)=f(96)f(101)=f(97)由f(1)=2，f(4)=f(0)得f(0)=2 所以f(101)=f(97)=f(100)=f(96)=2