Question

设函数f(x)的定义域为R，当x>0时，f(x)>1且对任意的x,y∈R有f(x+y)=f(x)f(y)，f(1)=2,求对任意的x∈R

都有f(x)>0

Answer 1

令x = 0,y = 1,由等式得f(1) = f(0)f(1),f(1) = 2,f(0) = 1 > 0
当x < 0,-x > 0,f(-x + x) = f(－x）f（x），f（－x）＞　1，有f（x）　＞　0