Question

设f(x)为R上奇函数,且f(x+2)=-f(x),当0

Answer 1

设f(x)为R上奇函数,且f(x+2)=-f(x),当0≤x≤1,f(x)=x,求f(7.5)

由f(x+2)=-f(x)有f(7.5)=f(5.5+2) = -f(5.5) = -f(3.5+2) = -[-f(3.5)] = f(3.5) =f(1.5+2) = -f(1.5) = -f(-0.5+2) = f(-0.5)

又因为f(x)为R上奇函数,所以有f(-x)=-f(x)

f(-0.5)=-f(0.5) 当0≤x≤1,f(x)=x ,f(0.5)=0.5

f(7.5)=-0.5