Question

设f(x)是(负无穷,正无穷)上的奇函数,f(x)+f(x+3)=0,当0≤x≤1时,f(x)=2^x-1,则f(5.5)+?

急。
是问、f(5.5)=?

Answer 1

f(x)=-f(x+3)
f(5.5)=-f(2.5+3)=f(2.5)=-f(-0.5+3)=f(-0.5)
奇函数
f(x)=-f(-x)
f(-0.5)=-f(0.5)=-(2^0.5-1)

Answer 2

∵f(x)+f(x+3)=0
∴f(x)=-f(x+3)
∴f(x-6)=-f(x-3)=f(x)
∴f(5.5)=f(5.5-6)=f(-0.5)=-f(0.5)=-2^(0.5)-1=-√2-1

Answer 3

f(x+3)=-f(x)
f(5.5)=f(2.5+3)=-f(2.5)=-f(-0.5+3)=-[-f(-0.5)]=f(-0.5)=-f(0.5)=-√2 -1