已知函数f(x)是偶函数,并且对于定义域内任意x,满足f(x+2）=-1/f(x),若当2

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f(x+2）=-1/f(x)
f(x+4)=-1/f(x+2)=f(x)
所以f(x)以4为周期的周期函数
f(2007.5)=f(2007.5-2008)=f(-0.5)=f(0.5)
f(x+2）=-1/f(x)
所以f(x)=-1/f(x+2)
f(0.5)=-1/f(2.5)=-1/2.5=-0.4
======以下答案可供参考======
供参考答案1:
f(x+4) = -1/f(x+2) = f(x)说明周期是4
f(2007.5) = f(2008 - 0.5) = f(-0.5)
f(-0.5)= f(0.5)偶函数
f(0.5) = -1/f(2 + 0.5) = -1/f(2.5) = -1/2.5