Real Analysis Help!!

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• Dec 4th 2008, 05:54 AM
mathprincess24
Real 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.
• Dec 4th 2008, 06:15 AM
ThePerfectHacker
Quote:

Originally Posted by mathprincess24
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.

See this.
• Dec 6th 2008, 12:06 PM
mathprincess24
how do i know that f(x) = e^x?
• Dec 6th 2008, 01:59 PM
ThePerfectHacker
Quote:

Originally Posted by mathprincess24
how do i know that f(x) = e^x?

From the "initial conditions" i.e. f(0)=1 and f(1)=e.
Do you see how?
• Dec 6th 2008, 06:38 PM
mathprincess24
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.