Question

已知函数f(x)的定义域为R，且满足f(a+b)=f(a)·f(b)）（a.b属于R）且f(x)>0,若f（1)=1/2,则f(-2)=

详细过程

Answer 1

f(1+0)=f(1)·f(0)=f(1)
f(0) =1;
f(1-1)=f(0)=f(-1)·f(1)=1
f(2-2)=f(0)=f(2).(f-2)=1
f(2) =f(1+1) =f(1).f(1) = 0.25
f(-2) = 4

Answer 2

f(0+1)=f(0)+f(1)
f(0)=f(0)·f(0)
f(0)=1
f(-1+1)=f(-1)+f(1)=1
f(-1)=1/2
f(-1-1)=f(-1)+f(-1)=1

Answer 3

图:

Answer 4

楼上正解 其实f(X)=(1/2）^x ,x为指数。

Answer 5

f(a+b)=f(a)·f(b)，且f(x)>0,令a,b=0，得到f(0)=1=f(x-x)=f(x)*f(-x),f(-x)=1/f(x),f(2)=f(1+1)=f(1)·f(1)=1/4,f(-2)=4