Question

设f(x)是(-∞,+∞)上的奇函数,且f(x+2)=-f(x),当0≤x≤1时,f(x)=x.则f(47.5)等于多少?

求数学大神解答~~~~~

Answer 1

f(x+2)=-f(x)

所以f(x+4)=f(x+2+2)=-f(x+2)=f(x)
所以f(x)是以4 为周期的周期函数
所以f(47.5)=f(-0.5)=-f(0.5)=-0.5

Answer 2

f(-x)=-f(x)
f(x+4)=f(x+2+2)=-f(x+2)=f(x)

f(47.5)=f(-0.5+4*12)=f(-0.5)=-f(0.5)=-0.5