Question

已知定义域为R的函数f(x)满足f(a+b)=f(a)·f(b)(a、b∈R)且f(x)＞0,若f(1)= ,则f(-2)等于(    )

A.2                 B.4              C.                  D.

Answer 1

B

解析：由f(a+b)=f(a)·f(b),知f(0+0)=f²(0)f(0)=1(f(x)＞0),

又f(2)=f(1+1)=f²(1)=,

f(2-2)=f(2)·f(-2)=f(0)=1f(-2)==4.