Thanks for the explaination.....

passion4ivymba wrote:

if f(x)>0 and f(x+y)=f(x)f(y) for all x,y. Then f(2) =?

Some information is missing here.

You get \(f(0+0) = f(0)^2\)

\(f(0)[f(0) - 1] = 0\)

\(f(0) = 1\)

Then, you get infinite GPs each having a different value for f(2) depending on what value you choose for f(1).

Say f(1) = 2

... f(-3) = 1/8, f(-2) = 1/4, f(-1) = 1/2, f(0) = 1, f(1) = 2, f(2) = 4, f(3) = 8 and so on

Say f(1) = 3

...f(-3) = 1/27, f(-2) = 1/9, f(-1) = 1/3, f(0) = 1, f(1) = 3, f(2) = 9, f(3) = 27 and so on