二次函数f(x)满足f(1)=2,且对任意x,y都有f(x-y)=f(x)/f(y)

f(y-x)=f(-(x-y))=f(y)/f(x)
f(y-x)f(x-y)=1
t=x-y,-t=y-x
f(t)f(-t)=1
原式=f(5)f(4)f(3)f(2)f(1)f(0)f(-1)f(-2)f(-3)f(-4)
f(4)f(-4)=1,f(3)f(-3)=1,f(2)f(-2)=1,f(1)f(-1)=1
原式=f(5)f(0)
x=1,y=0
f(1)=f(1)/f(0)
f(0)=1
x=2,y=1
f(2-1)=f(2)/f(1)=f(1)
f(2)=f(1)^2=2^2=4
x=4,y=2
f(4-2)=f(4)/f(2)=f(2)
f(4)=f(2)^2=4^2=16
f(-1)=1/f(1)=1/2
f(5)=f(4+1)=f(4-(-1))=f(4)/f(-1)==f(4)f(1)=16*2=32
选D.