So f(2x)=2f(x)

And because x>0, f (x)

f(2x)-f(x)= f(x)& lt； 0

So f (2x) < f(x)

And because 2x>x>0

So f(x) is a monotonically decreasing function.

2. Because f(x) satisfies f(a+b)=f(a)+f(b) for all real numbers.

So when A = 3 and B = 0, f(3)=f(3)+f(0).

So f(0)=0.

Yes, because b=-a is desirable.

Then f(0)=f(a)+f(-a)=0.

So f(a)=-f(-a)

So f(x) is odd function.