函数f(x)对任意实数x满足条件f(x 1)=1/f(x)若f(1)=-5,则f[f(5)]=?

f(x 2)=f[(x 1) 1]

=1/f(x 1)

=1/[1/f(x)]

=f(x)

所以f(5)=f(3 2)=f(3)=f(1 2)=f(1)=-5

f[f(5)]=f(-5)=f(-5 2)=f(-3)

=f(-3 2)=f(-1)=f(-1 2)=f(1)=-5