Question

1.设f(x)s是R上的奇函数,且满足f(x+2)=-f(x),当0≤x≤1时,f(x)=x,则f(3.5)=?

Answer 1

满足f(x+2)=-f(x),

f(3.5)=f(1.5+2)=-f(1.5)

f(1.5)=f(-0.5+2)=-f(-0.5)

f(3.5)=f(-0.5)

f(x)s是R上的奇函数,f(-0.5)=-f(0.5)

当0≤x≤1时,f(x)=x,f(0.5)=0.5

f(3.5)=f(-0.5)=-f(0.5)=-0.5

2.若f(1/x)=1/(x+1)=(1/x)/[1+1/x]

则f(x)=x/(x+1)