设f(x)在(-∞,+∞)上是奇函数,f(x+2)=-f(x),当0≤x≤1时,f(x)=x,则f(7.5)等于 ( )A. 0.5B. -0.5C. 1.5D. -1.5
热心网友
答案为B解答如下:由f(x+2)=-f(x),可得f(7.5)=-f(5.5)=-{-f(3.5)}=f(3.5)=-f(1.5)而f(1.5)=f(-0.5+2)=-f(-0.5)而f(x)是(-∞,+∞)的奇函数,所以f(-0.5)=-f(0.5)故f(7.5)=-f(0.5)=-0.5
热心网友
设f(x)在(-∞,+∞)上是奇函数,f(x+2)=-f(x),当0≤x≤1时,f(x)=x,则f(7.5)等于 ( )A. 0.5B. -0.5C. 1.5D. -1.5 解：有已知，f(x+2)=-f(x),故f(7.5)=-f(5.5)＝-（-f(3.5))=f(3.5)=-f(1.5)=-(-f(-0.5))=f(-0.5)又f(x)在(-∞,+∞)上是奇函数所以f(-0.5)=-f(0.5)=-0.5故选B .