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)=?2.若f(1/x)=1/(x+1),则f(x)=?
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)=?
2.若f(1/x)=1/(x+1),则f(x)=?
当x=0.5时,f(x)=0.5,因为f(x)为奇函数,所以-f(x)=f(-x)即 -f(0.5)=f(-0.5)=-0.5,又f(1.5)=-f(0.5)=-0.5, -f(1.5)=0.5,所以f(3.5)=-f(1.5)=0.5
f(x)=f[1/(1/x)]=1/(1/x+1)=x/(x+1),反正就是用(1/x)把x换掉就行了
1.由题意知f(x)=x (-1≤x≤1),∵ f(x+2)=-f(x),∴f(x+4)=f(x),∴f(x)=x-4 (3≤x≤5),∴f(3.5)=-0.5
2.∵f(1/x)=1/(x+1),设t=1/x,则x=1/t,f(t)=1/[(1/t)+1]=t/(t+1),∴f(x)=x/(x+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)=0.5f(3.5)=f(-0.5)=-f(0.5)=-0.52.若f(1/x)=1/(x+1)=(1/x)/[1+1/x...
(1)f(3.5)=f(1.5+2)=-f(1.5)=-f(-0.5+2)=-(-f(-0.5))=-f(0.5)=-0.5;
(2)令t=1/x (t不等于0),则x=1/t
则f(t)=1/(1/t+1)=t/(t+1)
所以f(x)=x/(x+1)(x不等于0)