若f(x)满足f(x+1)=-(1/f(x)),当x∈[0,2]时,f(x)=(x-1)²,求f(3),f(-7/2)的值.

问题描述:

若f(x)满足f(x+1)=-(1/f(x)),当x∈[0,2]时,f(x)=(x-1)²,求f(3),f(-7/2)的值.

f(3)=f(2+1)=-1/f(2)=-1
f(x)=-1/f(x+1)
f(-7/2)=-1/f(-5/2)=f(-3/2)=-1/f(1/2)=-4