Question

抽象函数求解函数f（x）对于任意实数x满足条件f（x+2）=1/f（x）,若f（1）=-5 则F[f（5）]=_____

Answer 1

f（x+2）=1/f（x),f（1）=-5

所以f(1+2)=1/f(1) =>f(3)=-1/5

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

f（x+2）=1/f（x) =>f(x)=1/f(x+2)

F[f（5）]=F(-5)=1/f(-5+2)=1/f(-3)=f(-3+2)=f(-1)=1/f(-1+2)=1/f(1)=-1/5

仔细点看下公式的变换,应该明白了!