f(x)是偶函数满足f(x+2)=-1/f(x)当2≤x≤3 时,f(x)=x+1,则f(5.5)=同上
问题描述：
f(x)是偶函数满足f(x+2)=-1/f(x)当2≤x≤3 时,f(x)=x+1,则f(5.5)=
同上
答
F(3.5)=F(-3.5)=-1/F(-1.5).
F(-1.5)=-1/F(0.5).
F(0.5)=-1/F(2.5)
F(2.5)=3.5
则F(3.5)=3.5
答
f(5.5)=f(3.5+2)=-1/f(3.5)
f(3.5)=f(1.5+2)=-1/f(1.5)
因为当2≤x≤3 时,f(x)=x+1。所以f(1.5)=2.5
f(3.5)=-1/f(1.5)=-1/2.5
f(5.5)=-1/f(3.5)=2.5
答
应为f(X)是偶函数,所以f(-X) = f(X)
f(5.5)=f(2+2+2+2-2.5)
=-1/f(2+2+2-2.5)
=f(2+2-2.5)
=-1/f(2-2.5)
=f(-2.5)
=f(2.5)
=2.5+1
=3.5
答
f(x+2)=-1/f(x)=f(x-2)所以周期为4
f(5.5)=f(1.5)=f(-2.5)=f(2.5)=2.5+1=3.5