若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?

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若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?若函数f(x)满足f(x+10)=2

若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?
若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?

若函数f(x)满足f(x+10)=2f(x+9),且f(0)=1,f(-10)=?
x=-10,得f(0)=2f(-1)
x=-11,得f(-1=2f(-2)
x=-12,得f(-2)=2f(-3)
……
x=-19,得f(-9)=2f(-10)
故1=f(0)=2f(-1)=2^2f(-2)=……=2^10f(-10)
故f(-10)=1/2^10=2^(-10)=1/1024

f(x+10)=2f(x+9)
f(x)=2f(x-1)=2[2f(x-1)]=2^2f(x-1)=4[2f(x-2)]=2^3f(x-2)=……=2^11f(x-10)=……=2^(n+1)f(x-n)
∴f(0)=2^11f(-10)=1
∴f(-10)=2^(-11)