Question

已知函数定义在R上的偶函数f(x)满足f(x+2)乘f(x)=1,且f(x)大于0,求f(119),

Answer 1

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

f(x+4) * f(x+2) = 1

∴ f(x+4) = f(x) 即 f(x) 周期为4

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

令x=-1

f(1)*f(-1) =1

又f(x)是偶函数,∴f(-1)=f(1)

且f(x) >0

∴f(-1) = f(1) = 1

f(119) = f(30*4 -1) = f(-1) = 1