Question

已知函数f(x)满足f(a+b)=f(a)*f(b),且f(x)>0,若f(1)=1/2,则f(-2)等于???

Answer 1

已知函数f(x)满足f(a+b)=f(a)*f(b),且f(x)>0,若f(1)=1/2,则f(-2)等于???
解析：∵函数f(x)满足f(a+b)=f(a)*f(b),且f(x)>0,若f(1)=1/2
f(1+0)=f(1)*f(0)=1/2==>f(0)=1
f(1-1)=f(1)*f(-1)=1==>f(-1)=2
f(-2)=f(-1-1)=f(-1)*f(-1)=2*2=4

Answer 2

f(x)满足f(a+b)=f(a)*f(b),
设A=0 B=0 则有F(0)=F(0)*F(0)==>F(0)=1或F(0)=0 F(0)=0 不合题意,舍
所以F(0)=1
设A=-1 B=1 则有F(0)=F(-1)*F(1) ==>F(-1)=2
设A=-1 B=-1则有F(-2)=F(-1)*F(-1)=2*2=4