Question

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(5)=___________

Answer 1

f(x+2)=1/f(x), f(x)=1/f(x+2)

f(x+2+2)=1/f(x+2)=f(x)

x=1, f(x)=f(1)=5

f(5)=f(1+2+2)=f(1)=5

f(f(5))=f(5)=f(1)=5