This one has been bothering me for days now. Can anyone help??

Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x.

Printable View

- December 4th 2008, 05:54 AMmathprincess24Real Analysis Help!!
This one has been bothering me for days now. Can anyone help??

Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x. - December 4th 2008, 06:15 AMThePerfectHacker
See this.

- December 6th 2008, 12:06 PMmathprincess24
how do i know that f(x) = e^x?

- December 6th 2008, 01:59 PMThePerfectHacker
- December 6th 2008, 06:38 PMmathprincess24
yes i understand that when you plug in e^x as the function that all the conditions are met, but how do i prove that its the only one that works. I'm not sure i understand the proof on the bottom half of the link you responded with.